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order</title> <meta name="description" content="Search results for: fractional order"> <meta name="keywords" content="fractional order"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="fractional order"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 13835</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: fractional order</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13835</span> Fractional Order Differentiator Using Chebyshev Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Koushlendra%20Kumar%20Singh">Koushlendra Kumar Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Manish%20Kumar%20Bajpai"> Manish Kumar Bajpai</a>, <a href="https://publications.waset.org/abstracts/search?q=Rajesh%20Kumar%20Pandey"> Rajesh Kumar Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A discrete time fractional orderdifferentiator has been modeled for estimating the fractional order derivatives of contaminated signal. The proposed approach is based on Chebyshev’s polynomials. We use the Riemann-Liouville fractional order derivative definition for designing the fractional order SG differentiator. In first step we calculate the window weight corresponding to the required fractional order. Then signal is convoluted with this calculated window’s weight for finding the fractional order derivatives of signals. Several signals are considered for evaluating the accuracy of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20order%20derivative" title="fractional order derivative">fractional order derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=chebyshev%0D%0Apolynomials" title=" chebyshev polynomials"> chebyshev polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=signals" title=" signals"> signals</a>, <a href="https://publications.waset.org/abstracts/search?q=S-G%20differentiator" title=" S-G differentiator"> S-G differentiator</a> </p> <a href="https://publications.waset.org/abstracts/21346/fractional-order-differentiator-using-chebyshev-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21346.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">648</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13834</span> Design Fractional-Order Terminal Sliding Mode Control for Synchronization of a Class of Fractional-Order Chaotic Systems with Uncertainty and External Disturbances</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shabnam%20Pashaei">Shabnam Pashaei</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammadali%20Badamchizadeh"> Mohammadali Badamchizadeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a new fractional-order terminal sliding mode control for synchronization of two different fractional-order chaotic systems with uncertainty and external disturbances. A fractional-order integral type nonlinear switching surface is presented. Then, using the Lyapunov stability theory and sliding mode theory, a fractional-order control law is designed to synchronize two different fractional-order chaotic systems. Finally, a simulation example is presented to illustrate the performance and applicability of the proposed method. Based on numerical results, the proposed controller ensures that the states of the controlled fractional-order chaotic response system are asymptotically synchronized with the states of the drive system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=terminal%20sliding%20mode%20control" title="terminal sliding mode control">terminal sliding mode control</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional-order%20calculus" title=" fractional-order calculus"> fractional-order calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=chaotic%20systems" title=" chaotic systems"> chaotic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=synchronization" title=" synchronization"> synchronization</a> </p> <a href="https://publications.waset.org/abstracts/67276/design-fractional-order-terminal-sliding-mode-control-for-synchronization-of-a-class-of-fractional-order-chaotic-systems-with-uncertainty-and-external-disturbances" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67276.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">409</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13833</span> Caputo-Type Fuzzy Fractional Riccati Differential Equations with Fuzzy Initial Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Trilok%20Mathur">Trilok Mathur</a>, <a href="https://publications.waset.org/abstracts/search?q=Shivi%20Agarwal"> Shivi Agarwal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Caputo-type%20fuzzy%20fractional%20derivative" title="Caputo-type fuzzy fractional derivative">Caputo-type fuzzy fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=Fractional%20Riccati%20differential%20equations" title=" Fractional Riccati differential equations"> Fractional Riccati differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Laplace-Adomian-Pade%20method" title=" Laplace-Adomian-Pade method"> Laplace-Adomian-Pade method</a>, <a href="https://publications.waset.org/abstracts/search?q=Mittag%20Leffler%20function" title=" Mittag Leffler function"> Mittag Leffler function</a> </p> <a href="https://publications.waset.org/abstracts/51080/caputo-type-fuzzy-fractional-riccati-differential-equations-with-fuzzy-initial-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51080.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">395</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13832</span> Fractional Calculus into Structural Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Lopez">Jorge Lopez</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we introduce fractional calculus in order to study the dynamics of a damped multistory building with some symmetry. Initially we make a review of the dynamics of a free and damped multistory building. Then we introduce those concepts of fractional calculus that will be involved in our study. It has been noticed that fractional calculus provides models with less parameters than those based on classical calculus. In particular, a damped classical oscilator is more naturally described by using fractional derivatives. Accordingly, we model our multistory building as a set of coupled fractional oscillators and compare its dynamics with the results coming from traditional methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=coupled%20oscillators" title="coupled oscillators">coupled oscillators</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculus" title=" fractional calculus"> fractional calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20oscillator" title=" fractional oscillator"> fractional oscillator</a>, <a href="https://publications.waset.org/abstracts/search?q=structural%20dynamics" title=" structural dynamics"> structural dynamics</a> </p> <a href="https://publications.waset.org/abstracts/124822/fractional-calculus-into-structural-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124822.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">242</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13831</span> Commutativity of Fractional Order Linear Time-Varying Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Salisu%20Ibrahim">Salisu Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of MATLAB (Simulink). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20differential%20equation" title="fractional differential equation">fractional differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=physical%20systems" title=" physical systems"> physical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=equivalent%20circuit" title=" equivalent circuit"> equivalent circuit</a>, <a href="https://publications.waset.org/abstracts/search?q=analog%20control" title=" analog control"> analog control</a> </p> <a href="https://publications.waset.org/abstracts/171951/commutativity-of-fractional-order-linear-time-varying-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171951.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">114</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13830</span> Commutativity of Fractional Order Linear Time-Varying System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Salisu%20Ibrahim">Salisu Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of Matlab (Simulink). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20differential%20equation" title="fractional differential equation">fractional differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=physical%20systems" title=" physical systems"> physical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=equivalent%20circuit" title=" equivalent circuit"> equivalent circuit</a>, <a href="https://publications.waset.org/abstracts/search?q=and%20analog%20control" title=" and analog control"> and analog control</a> </p> <a href="https://publications.waset.org/abstracts/172277/commutativity-of-fractional-order-linear-time-varying-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/172277.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">77</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13829</span> Derivation of Fractional Black-Scholes Equations Driven by Fractional G-Brownian Motion and Their Application in European Option Pricing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Changhong%20Guo">Changhong Guo</a>, <a href="https://publications.waset.org/abstracts/search?q=Shaomei%20Fang"> Shaomei Fang</a>, <a href="https://publications.waset.org/abstracts/search?q=Yong%20He"> Yong He</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=European%20option%20pricing" title="European option pricing">European option pricing</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20Black-Scholes%20equations" title=" fractional Black-Scholes equations"> fractional Black-Scholes equations</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20g-Brownian%20motion" title=" fractional g-Brownian motion"> fractional g-Brownian motion</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%27s%20series%20of%20fractional%20order" title=" Taylor's series of fractional order"> Taylor's series of fractional order</a>, <a href="https://publications.waset.org/abstracts/search?q=uncertain%20volatility" title=" uncertain volatility"> uncertain volatility</a> </p> <a href="https://publications.waset.org/abstracts/127107/derivation-of-fractional-black-scholes-equations-driven-by-fractional-g-brownian-motion-and-their-application-in-european-option-pricing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127107.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">163</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13828</span> Numerical Solutions of Fractional Order Epidemic Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sadia%20Arshad">Sadia Arshad</a>, <a href="https://publications.waset.org/abstracts/search?q=Ayesha%20Sohail"> Ayesha Sohail</a>, <a href="https://publications.waset.org/abstracts/search?q=Sana%20Javed"> Sana Javed</a>, <a href="https://publications.waset.org/abstracts/search?q=Khadija%20Maqbool"> Khadija Maqbool</a>, <a href="https://publications.waset.org/abstracts/search?q=Salma%20Kanwal"> Salma Kanwal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The dynamical study of the carriers play an essential role in the evolution and global transmission of infectious diseases and will be discussed in this study. To make this approach novel, we will consider the fractional order model which is generalization of integer order derivative to an arbitrary number. Since the integration involved is non local therefore this property of fractional operator is very useful to study epidemic model for infectious diseases. An extended numerical method (ODE solver) is implemented on the model equations and we will present the simulations of the model for diﬀerent values of fractional order to study the eﬀect of carriers on transmission dynamics. Global dynamics of fractional model are established by using the reproduction number. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fractional%20di%EF%AC%80erential%20equation" title="Fractional diﬀerential equation">Fractional diﬀerential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Numerical%20simulations" title=" Numerical simulations"> Numerical simulations</a>, <a href="https://publications.waset.org/abstracts/search?q=epidemic%20model" title=" epidemic model"> epidemic model</a>, <a href="https://publications.waset.org/abstracts/search?q=transmission%20dynamics" title=" transmission dynamics"> transmission dynamics</a> </p> <a href="https://publications.waset.org/abstracts/17447/numerical-solutions-of-fractional-order-epidemic-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17447.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">600</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13827</span> Lyapunov Type Inequalities for Fractional Impulsive Hamiltonian Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kazem%20Ghanbari">Kazem Ghanbari</a>, <a href="https://publications.waset.org/abstracts/search?q=Yousef%20Gholami"> Yousef Gholami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with study about fractional order impulsive Hamiltonian systems and fractional impulsive Sturm-Liouville type problems derived from these systems. The main purpose of this paper devotes to obtain so called Lyapunov type inequalities for mentioned problems. Also, in view point on applicability of obtained inequalities, some qualitative properties such as stability, disconjugacy, nonexistence and oscillatory behaviour of fractional Hamiltonian systems and fractional Sturm-Liouville type problems under impulsive conditions will be derived. At the end, we want to point out that for studying fractional order Hamiltonian systems, we will apply recently introduced fractional Conformable operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20derivatives%20and%20integrals" title="fractional derivatives and integrals">fractional derivatives and integrals</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamiltonian%20system" title=" Hamiltonian system"> Hamiltonian system</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov-type%20inequalities" title=" Lyapunov-type inequalities"> Lyapunov-type inequalities</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=disconjugacy" title=" disconjugacy"> disconjugacy</a> </p> <a href="https://publications.waset.org/abstracts/48806/lyapunov-type-inequalities-for-fractional-impulsive-hamiltonian-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48806.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">354</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13826</span> Application of Fractional Model Predictive Control to Thermal System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aymen%20Rhouma">Aymen Rhouma</a>, <a href="https://publications.waset.org/abstracts/search?q=Khaled%20Hcheichi"> Khaled Hcheichi</a>, <a href="https://publications.waset.org/abstracts/search?q=Sami%20Hafsi"> Sami Hafsi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller<em>.</em> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20model%20predictive%20control" title="fractional model predictive control">fractional model predictive control</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20order%20systems" title=" fractional order systems"> fractional order systems</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20system" title=" thermal system"> thermal system</a>, <a href="https://publications.waset.org/abstracts/search?q=predictive%20control" title=" predictive control"> predictive control</a> </p> <a href="https://publications.waset.org/abstracts/66187/application-of-fractional-model-predictive-control-to-thermal-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66187.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">411</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13825</span> Fractional Order Sallen-Key Filters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Soltan">Ahmed Soltan</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20G.%20Radwan"> Ahmed G. Radwan</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20M.%20Soliman"> Ahmed M. Soliman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which are unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples of the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sallen-Key" title="Sallen-Key">Sallen-Key</a>, <a href="https://publications.waset.org/abstracts/search?q=fractance" title=" fractance"> fractance</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=low-pass%20filter" title=" low-pass filter"> low-pass filter</a>, <a href="https://publications.waset.org/abstracts/search?q=analog%20filter" title=" analog filter"> analog filter</a> </p> <a href="https://publications.waset.org/abstracts/2170/fractional-order-sallen-key-filters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2170.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">715</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13824</span> Modified Fractional Curl Operator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rawhy%20Ismail">Rawhy Ismail </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Applying fractional calculus in the field of electromagnetics shows significant results. The fractionalization of the conventional curl operator leads to having additional solutions to an electromagnetic problem. This work restudies the concept of the fractional curl operator considering fractional time derivatives in Maxwell’s curl equations. In that sense, a general scheme for the wave loss term is introduced and the degree of freedom of the system is affected through imposing the new fractional parameters. The conventional case is recovered by setting all fractional derivatives to unity. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=curl%20operator" title="curl operator">curl operator</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculus" title=" fractional calculus"> fractional calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20curl%20operators" title=" fractional curl operators"> fractional curl operators</a>, <a href="https://publications.waset.org/abstracts/search?q=Maxwell%20equations" title=" Maxwell equations"> Maxwell equations</a> </p> <a href="https://publications.waset.org/abstracts/35772/modified-fractional-curl-operator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35772.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">487</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13823</span> A New Study on Mathematical Modelling of COVID-19 with Caputo Fractional Derivative</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sadia%20Arshad">Sadia Arshad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculus" title="fractional calculus">fractional calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=modeling" title=" modeling"> modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20solution" title=" numerical solution"> numerical solution</a> </p> <a href="https://publications.waset.org/abstracts/151862/a-new-study-on-mathematical-modelling-of-covid-19-with-caputo-fractional-derivative" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/151862.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">111</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13822</span> Numerical Solution of Space Fractional Order Solute Transport System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shubham%20Jaiswal">Shubham Jaiswal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=spatial%20fractional%20order%20advection-dispersion%20equation" title="spatial fractional order advection-dispersion equation">spatial fractional order advection-dispersion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=second-kind%20shifted%20Chebyshev%20polynomial" title=" second-kind shifted Chebyshev polynomial"> second-kind shifted Chebyshev polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title=" collocation method"> collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=conservative%20system" title=" conservative system"> conservative system</a>, <a href="https://publications.waset.org/abstracts/search?q=non-conservative%20system" title=" non-conservative system"> non-conservative system</a> </p> <a href="https://publications.waset.org/abstracts/80604/numerical-solution-of-space-fractional-order-solute-transport-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/80604.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">261</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13821</span> Relation between Roots and Tangent Lines of Function in Fractional Dimensions: A Method for Optimization Problems </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Dorostkar">Ali Dorostkar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=tangent%20line" title="tangent line">tangent line</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20dimension" title=" fractional dimension"> fractional dimension</a>, <a href="https://publications.waset.org/abstracts/search?q=root" title=" root"> root</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization%20problem" title=" optimization problem"> optimization problem</a> </p> <a href="https://publications.waset.org/abstracts/94257/relation-between-roots-and-tangent-lines-of-function-in-fractional-dimensions-a-method-for-optimization-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/94257.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">192</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13820</span> Melnikov Analysis for the Chaos of the Nonlocal Nanobeam Resting on Fractional-Order Softening Nonlinear Viscoelastic Foundations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Guy%20Joseph%20Eyebe">Guy Joseph Eyebe</a>, <a href="https://publications.waset.org/abstracts/search?q=Gambo%20Betchewe"> Gambo Betchewe</a>, <a href="https://publications.waset.org/abstracts/search?q=Alidou%20Mohamadou"> Alidou Mohamadou</a>, <a href="https://publications.waset.org/abstracts/search?q=Timoleon%20Crepin%20Kofane"> Timoleon Crepin Kofane</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chaos" title="chaos">chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional-order" title=" fractional-order"> fractional-order</a>, <a href="https://publications.waset.org/abstracts/search?q=Melnikov%20method" title=" Melnikov method"> Melnikov method</a>, <a href="https://publications.waset.org/abstracts/search?q=nanobeam" title=" nanobeam"> nanobeam</a> </p> <a href="https://publications.waset.org/abstracts/102726/melnikov-analysis-for-the-chaos-of-the-nonlocal-nanobeam-resting-on-fractional-order-softening-nonlinear-viscoelastic-foundations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/102726.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">159</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13819</span> Backstepping Design and Fractional Differential Equation of Chaotic System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ayub%20Khan">Ayub Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Net%20Ram%20Garg"> Net Ram Garg</a>, <a href="https://publications.waset.org/abstracts/search?q=Geeta%20Jain"> Geeta Jain</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=backstepping%20method" title="backstepping method">backstepping method</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20order" title=" fractional order"> fractional order</a>, <a href="https://publications.waset.org/abstracts/search?q=synchronization" title=" synchronization"> synchronization</a>, <a href="https://publications.waset.org/abstracts/search?q=chaotic%20system" title=" chaotic system "> chaotic system </a> </p> <a href="https://publications.waset.org/abstracts/6438/backstepping-design-and-fractional-differential-equation-of-chaotic-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/6438.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">457</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13818</span> An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Haniye%20Dehestani">Haniye Dehestani</a>, <a href="https://publications.waset.org/abstracts/search?q=Yadollah%20Ordokhani"> Yadollah Ordokhani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title="collocation method">collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20partial%20differential%20equations" title=" fractional partial differential equations"> fractional partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=legendre-laguerre%20functions" title=" legendre-laguerre functions"> legendre-laguerre functions</a>, <a href="https://publications.waset.org/abstracts/search?q=pseudo-operational%20matrix%20of%20integration" title=" pseudo-operational matrix of integration"> pseudo-operational matrix of integration</a> </p> <a href="https://publications.waset.org/abstracts/97195/an-efficient-collocation-method-for-solving-the-variable-order-time-fractional-partial-differential-equations-arising-from-the-physical-phenomenon" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/97195.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">166</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13817</span> Solutions of Fractional Reaction-Diffusion Equations Used to Model the Growth and Spreading of Biological Species</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kamel%20Al-Khaled">Kamel Al-Khaled</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some ﬁelds such as cell biology, chemistry, physics, and ﬁnance, makes it necessary to apply the results reported here to some numerical examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20partial%20differential%20equations" title="fractional partial differential equations">fractional partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=reaction-di%EF%AC%80usion%20equations" title=" reaction-diﬀusion equations"> reaction-diﬀusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=adomian%20decomposition" title=" adomian decomposition"> adomian decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=biological%20species" title=" biological species"> biological species</a> </p> <a href="https://publications.waset.org/abstracts/55994/solutions-of-fractional-reaction-diffusion-equations-used-to-model-the-growth-and-spreading-of-biological-species" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55994.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">375</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13816</span> Observer-Based Leader-Following Consensus of Nonlinear Fractional-Order Multi-Agent Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Afaghi">Ali Afaghi</a>, <a href="https://publications.waset.org/abstracts/search?q=Sehraneh%20Ghaemi"> Sehraneh Ghaemi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The coordination of the multi-agent systems has been one of the interesting topic in recent years, because of its potential applications in many branches of science and engineering such as sensor networks, flocking, underwater vehicles and etc. In the most of the related studies, it is assumed that the dynamics of the multi-agent systems are integer-order and linear and the multi-agent systems with the fractional-order nonlinear dynamics are rarely considered. However many phenomena in nature cannot be described within integer-order and linear characteristics. This paper investigates the leader-following consensus problem for a class of nonlinear fractional-order multi-agent systems based on observer-based cooperative control. In the system, the dynamics of each follower and leader are nonlinear. For a multi-agent system with fixed directed topology firstly, an observer-based consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on the property of the stability theory of fractional-order system, some sufficient conditions are presented for the asymptotical stability of the observer-based fractional-order control systems. The proposed method is applied on a five-agent system with the fractional-order nonlinear dynamics and unavailable states. The simulation example shows that the proposed scenario results in the good performance and can be used in many practical applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional-order%20multi-agent%20systems" title="fractional-order multi-agent systems">fractional-order multi-agent systems</a>, <a href="https://publications.waset.org/abstracts/search?q=leader-following%20consensus" title=" leader-following consensus"> leader-following consensus</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20dynamics" title=" nonlinear dynamics"> nonlinear dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=directed%20graphs" title=" directed graphs"> directed graphs</a> </p> <a href="https://publications.waset.org/abstracts/67272/observer-based-leader-following-consensus-of-nonlinear-fractional-order-multi-agent-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67272.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">398</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13815</span> A Dynamical Study of Fractional Order Obesity Model by a Combined Legendre Wavelet Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hakiki%20Kheira">Hakiki Kheira</a>, <a href="https://publications.waset.org/abstracts/search?q=Belhamiti%20Omar"> Belhamiti Omar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we propose a new compartmental fractional order model for the simulation of epidemic obesity dynamics. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. We also present some fractional differential illustrative examples to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Caputo%20derivative" title="Caputo derivative">Caputo derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=epidemiology" title=" epidemiology"> epidemiology</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20wavelet%20method" title=" Legendre wavelet method"> Legendre wavelet method</a>, <a href="https://publications.waset.org/abstracts/search?q=obesity" title=" obesity "> obesity </a> </p> <a href="https://publications.waset.org/abstracts/42731/a-dynamical-study-of-fractional-order-obesity-model-by-a-combined-legendre-wavelet-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42731.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">420</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13814</span> Fractional-Order PI Controller Tuning Rules for Cascade Control System </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Truong%20Nguyen%20Luan%20Vu">Truong Nguyen Luan Vu</a>, <a href="https://publications.waset.org/abstracts/search?q=Le%20Hieu%20Giang"> Le Hieu Giang</a>, <a href="https://publications.waset.org/abstracts/search?q=Le%20Linh"> Le Linh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bode%E2%80%99s%20ideal%20transfer%20function" title="Bode’s ideal transfer function">Bode’s ideal transfer function</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculus" title=" fractional calculus"> fractional calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%E2%80%93order%20proportional%20integral%20%28FOPI%29%20controller" title=" fractional–order proportional integral (FOPI) controller"> fractional–order proportional integral (FOPI) controller</a>, <a href="https://publications.waset.org/abstracts/search?q=cascade%20control%20system" title=" cascade control system"> cascade control system</a> </p> <a href="https://publications.waset.org/abstracts/48740/fractional-order-pi-controller-tuning-rules-for-cascade-control-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48740.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">377</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13813</span> Nonlocal Phenomena in Quantum Mechanics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kazim%20G.%20Atman">Kazim G. Atman</a>, <a href="https://publications.waset.org/abstracts/search?q=H%C3%BCseyin%20Sirin"> Hüseyin Sirin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In theoretical physics, nonlocal phenomena has always been subject of debate. However, in the conventional mathematical approach where the developments of the physical systems are investigated by using the standard mathematical tools, nonlocal effects are not taken into account. In order to investigate the nonlocality in quantum mechanics and fractal property of space, fractional derivative operators are employed in this study. In this manner, fractional creation and annihilation operators are introduced and Einstein coefficients are taken into account as an application of concomitant formalism in quantum field theory. Therefore, each energy mode of photons are considered as fractional quantized harmonic oscillator hereby Einstein coefficients are obtained. Nevertheless, wave function and energy eigenvalues of fractional quantum mechanical harmonic oscillator are obtained via the fractional derivative order α which is a measure of the influence of nonlocal effects. In the case α = 1, where space becomes homogeneous and continuous, standard physical conclusions are recovered. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Einstein%E2%80%99s%20Coefficients" title="Einstein’s Coefficients">Einstein’s Coefficients</a>, <a href="https://publications.waset.org/abstracts/search?q=Fractional%20Calculus" title=" Fractional Calculus"> Fractional Calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=Fractional%20Quantum%20Mechanics" title=" Fractional Quantum Mechanics"> Fractional Quantum Mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=Nonlocal%20Theories" title=" Nonlocal Theories"> Nonlocal Theories</a> </p> <a href="https://publications.waset.org/abstracts/124566/nonlocal-phenomena-in-quantum-mechanics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124566.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">169</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13812</span> Analytical Solutions of Time Space Fractional, Advection-Dispersion and Whitham-Broer-Kaup Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Danish%20Khan">Muhammad Danish Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Imran%20Naeem"> Imran Naeem</a>, <a href="https://publications.waset.org/abstracts/search?q=Mudassar%20Imran"> Mudassar Imran</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, we study time-space Fractional Advection-Dispersion (FADE) equation and time-space Fractional Whitham-Broer-Kaup (FWBK) equation that have a significant role in hydrology. We introduce suitable transformations to convert fractional order derivatives to integer order derivatives and as a result these equations transform into Partial Differential Equations (PDEs). Then the Lie symmetries and corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=modified%20Riemann-Liouville%20fractional%20derivative" title="modified Riemann-Liouville fractional derivative">modified Riemann-Liouville fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=lie-symmetries" title=" lie-symmetries"> lie-symmetries</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20system" title=" optimal system"> optimal system</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20solutions" title=" invariant solutions"> invariant solutions</a> </p> <a href="https://publications.waset.org/abstracts/2191/analytical-solutions-of-time-space-fractional-advection-dispersion-and-whitham-broer-kaup-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2191.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">431</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13811</span> Robust Fractional Order Controllers for Minimum and Non-Minimum Phase Systems – Studies on Design and Development</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Anand%20Kishore%20Kola">Anand Kishore Kola</a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20Uday%20Bhaskar%20Babu"> G. Uday Bhaskar Babu</a>, <a href="https://publications.waset.org/abstracts/search?q=Kotturi%20Ajay%20Kumar"> Kotturi Ajay Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The modern dynamic systems used in industries are complex in nature and hence the fractional order controllers have been contemplated as a fresh approach to control system design that takes the complexity into account. Traditional integer order controllers use integer derivatives and integrals to control systems, whereas fractional order controllers use fractional derivatives and integrals to regulate memory and non-local behavior. This study provides a method based on the maximumsensitivity (Ms) methodology to discover all resilient fractional filter Internal Model Control - proportional integral derivative (IMC-PID) controllers that stabilize the closed-loop system and deliver the highest performance for a time delay system with a Smith predictor configuration. Additionally, it helps to enhance the range of PID controllers that are used to stabilize the system. This study also evaluates the effectiveness of the suggested controller approach for minimum phase system in comparison to those currently in use which are based on Integral of Absolute Error (IAE) and Total Variation (TV). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=modern%20dynamic%20systems" title="modern dynamic systems">modern dynamic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20order%20controllers" title=" fractional order controllers"> fractional order controllers</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum-sensitivity" title=" maximum-sensitivity"> maximum-sensitivity</a>, <a href="https://publications.waset.org/abstracts/search?q=IMC-PID%20controllers" title=" IMC-PID controllers"> IMC-PID controllers</a>, <a href="https://publications.waset.org/abstracts/search?q=Smith%20predictor" title=" Smith predictor"> Smith predictor</a>, <a href="https://publications.waset.org/abstracts/search?q=IAE%20and%20TV" title=" IAE and TV"> IAE and TV</a> </p> <a href="https://publications.waset.org/abstracts/181141/robust-fractional-order-controllers-for-minimum-and-non-minimum-phase-systems-studies-on-design-and-development" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/181141.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">64</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13810</span> Tuning Fractional Order Proportional-Integral-Derivative Controller Using Hybrid Genetic Algorithm Particle Swarm and Differential Evolution Optimization Methods for Automatic Voltage Regulator System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fouzi%20Aboura">Fouzi Aboura</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The fractional order proportional-integral-derivative (FOPID) controller or fractional order (PIλDµ) is a proportional-integral-derivative (PID) controller where integral order (λ) and derivative order (µ) are fractional, one of the important application of classical PID is the Automatic Voltage Regulator (AVR).The FOPID controller needs five parameters optimization while the design of conventional PID controller needs only three parameters to be optimized. In our paper we have proposed a comparison between algorithms Differential Evolution (DE) and Hybrid Genetic Algorithm Particle Swarm Optimization (HGAPSO) ,we have studied theirs characteristics and performance analysis to find an optimum parameters of the FOPID controller, a new objective function is also proposed to take into account the relation between the performance criteria’s. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=FOPID%20controller" title="FOPID controller">FOPID controller</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20order" title=" fractional order"> fractional order</a>, <a href="https://publications.waset.org/abstracts/search?q=AVR%20system" title=" AVR system"> AVR system</a>, <a href="https://publications.waset.org/abstracts/search?q=objective%20function" title=" objective function"> objective function</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=GA" title=" GA"> GA</a>, <a href="https://publications.waset.org/abstracts/search?q=PSO" title=" PSO"> PSO</a>, <a href="https://publications.waset.org/abstracts/search?q=HGAPSO" title=" HGAPSO"> HGAPSO</a> </p> <a href="https://publications.waset.org/abstracts/164900/tuning-fractional-order-proportional-integral-derivative-controller-using-hybrid-genetic-algorithm-particle-swarm-and-differential-evolution-optimization-methods-for-automatic-voltage-regulator-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/164900.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">90</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13809</span> Anisotropic Total Fractional Order Variation Model in Seismic Data Denoising</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jianwei%20Ma">Jianwei Ma</a>, <a href="https://publications.waset.org/abstracts/search?q=Diriba%20Gemechu"> Diriba Gemechu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In seismic data processing, attenuation of random noise is the basic step to improve quality of data for further application of seismic data in exploration and development in different gas and oil industries. The signal-to-noise ratio of the data also highly determines quality of seismic data. This factor affects the reliability as well as the accuracy of seismic signal during interpretation for different purposes in different companies. To use seismic data for further application and interpretation, we need to improve the signal-to-noise ration while attenuating random noise effectively. To improve the signal-to-noise ration and attenuating seismic random noise by preserving important features and information about seismic signals, we introduce the concept of anisotropic total fractional order denoising algorithm. The anisotropic total fractional order variation model defined in fractional order bounded variation is proposed as a regularization in seismic denoising. The split Bregman algorithm is employed to solve the minimization problem of the anisotropic total fractional order variation model and the corresponding denoising algorithm for the proposed method is derived. We test the effectiveness of theproposed method for synthetic and real seismic data sets and the denoised result is compared with F-X deconvolution and non-local means denoising algorithm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=anisotropic%20total%20fractional%20order%20variation" title="anisotropic total fractional order variation">anisotropic total fractional order variation</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20order%20bounded%20variation" title=" fractional order bounded variation"> fractional order bounded variation</a>, <a href="https://publications.waset.org/abstracts/search?q=seismic%20random%20noise%20attenuation" title=" seismic random noise attenuation"> seismic random noise attenuation</a>, <a href="https://publications.waset.org/abstracts/search?q=split%20Bregman%20algorithm" title=" split Bregman algorithm"> split Bregman algorithm</a> </p> <a href="https://publications.waset.org/abstracts/77827/anisotropic-total-fractional-order-variation-model-in-seismic-data-denoising" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77827.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">207</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13808</span> Fractional Euler Method and Finite Difference Formula Using Conformable Fractional Derivative</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ramzi%20B.%20Albadarneh">Ramzi B. Albadarneh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conformable%20fractional%20derivative" title="conformable fractional derivative">conformable fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20formula" title=" finite difference formula"> finite difference formula</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20derivative" title=" fractional derivative"> fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20formula" title=" finite difference formula"> finite difference formula</a> </p> <a href="https://publications.waset.org/abstracts/37072/fractional-euler-method-and-finite-difference-formula-using-conformable-fractional-derivative" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37072.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">439</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13807</span> Dynamical Analysis of the Fractional-Order Mathematical Model of Hashimoto’s Thyroiditis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Neelam%20Singha">Neelam Singha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The present work intends to analyze the system dynamics of Hashimoto’s thyroiditis with the assistance of fractional calculus. Hashimoto’s thyroiditis or chronic lymphocytic thyroiditis is an autoimmune disorder in which the immune system attacks the thyroid gland, which gradually results in interrupting the normal thyroid operation. Consequently, the feedback control of the system gets disrupted due to thyroid follicle cell lysis. And, the patient perceives life-threatening clinical conditions like goiter, hyperactivity, euthyroidism, hyperthyroidism, etc. In this work, we aim to obtain the approximate solution to the posed fractional-order problem describing Hashimoto’s thyroiditis. We employ the Adomian decomposition method to solve the system of fractional-order differential equations, and the solutions obtained shall be useful to provide information about the effect of medical care. The numerical technique is executed in an organized manner to furnish the associated details of the progression of the disease and to visualize it graphically with suitable plots. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adomian%20decomposition%20method" title="adomian decomposition method">adomian decomposition method</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20derivatives" title=" fractional derivatives"> fractional derivatives</a>, <a href="https://publications.waset.org/abstracts/search?q=Hashimoto%27s%20thyroiditis" title=" Hashimoto's thyroiditis"> Hashimoto's thyroiditis</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematical%20modeling" title=" mathematical modeling"> mathematical modeling</a> </p> <a href="https://publications.waset.org/abstracts/139240/dynamical-analysis-of-the-fractional-order-mathematical-model-of-hashimotos-thyroiditis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/139240.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">211</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13806</span> Reduced Differential Transform Methods for Solving the Fractional Diffusion Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yildiray%20Keskin">Yildiray Keskin</a>, <a href="https://publications.waset.org/abstracts/search?q=Omer%20Acan"> Omer Acan</a>, <a href="https://publications.waset.org/abstracts/search?q=Murat%20Akkus"> Murat Akkus</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20diffusion%20equations" title="fractional diffusion equations">fractional diffusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo%20fractional%20derivative" title=" Caputo fractional derivative"> Caputo fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=reduced%20differential%20transform%20method" title=" reduced differential transform method"> reduced differential transform method</a>, <a href="https://publications.waset.org/abstracts/search?q=partial" title=" partial"> partial</a> </p> <a href="https://publications.waset.org/abstracts/17526/reduced-differential-transform-methods-for-solving-the-fractional-diffusion-equations" class="btn btn-primary btn-sm">Procedia</a> <a 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