Document Zbl 1528.45005

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Circ. Mat. Palermo (2)</a> <a href="/?q=in%3A496999" title="Articles in this Issue">72, No. 3, 1783-1795 (2023)</a>. </div> <div class="abstract">Summary: This paper investigates the existence and stability of random solutions of a class of Hadamard fractional order functional partial integral equations with random effects in Banach spaces.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7691132">Cited in <strong>14</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A45K05" title="MSC2020">45K05</a> </td> <td class="space"> Integro-partial differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A45R05" title="MSC2020">45R05</a> </td> <td class="space"> Random integral equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A45M10" title="MSC2020">45M10</a> </td> <td class="space"> Stability theory for integral equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A26A33" title="MSC2020">26A33</a> </td> <td class="space"> Fractional derivatives and integrals </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AHadamard+fractional+integral">Hadamard fractional integral</a>; <a href="/?q=ut%3Arandom+solution">random solution</a>; <a href="/?q=ut%3Astability">stability</a>; <a href="/?q=ut%3Aintegral+equation">integral equation</a>; <a href="/?q=ut%3Afixed+point">fixed point</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1528.45005" data-ciurl="/ci/07691132" data-biburl="/bibtex/07691132.bib" data-amsurl="/amsrefs/07691132.bib" data-xmlurl="/xml/07691132.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07691132.pdf" title="Zbl 1528.45005 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s12215-022-00770-7" aria-label="DOI for “Global stability results for Volterra-Hadamard random partial fractional integral equations”" title="10.1007/s12215-022-00770-7">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Abbas, S.; Albarakati, WA; Benchohra, M.; Hilal, EM, Global existence and stability results for partial fractional random differential equations, J. Appl. Anal., 21, 2, 79-87 (2015) · <a href="/1403.35310" class="nowrap">Zbl 1403.35310</a> · <a href="https://doi.org/10.1515/jaa-2015-0008" class="nowrap">doi:10.1515/jaa-2015-0008</a></td> </tr><tr> <td>[2]</td> <td class="space">Abbas, S.; Benchohra, M.; Graef, JR; Henderson, J., Implicit Fractional Differential and Integral Equations: existence and Stability (2018), Berlin: De Gruyter, Berlin · <a href="/1390.34002" class="nowrap">Zbl 1390.34002</a> · <a href="https://doi.org/10.1515/9783110553819" class="nowrap">doi:10.1515/9783110553819</a></td> </tr><tr> <td>[3]</td> <td class="space">Abbas, S.; Benchohra, M., Some stability concepts for Darboux problem for partial fractional differential equations on unbounded domain, Fixed Point Theory, 16, 1, 3-14 (2015) · <a href="/1333.35318" class="nowrap">Zbl 1333.35318</a></td> </tr><tr> <td>[4]</td> <td class="space">Abbas, S.; Benchohra, M., Nonlinear quadratic Volterra Riemann-Liouville integral equations of fractional order, Nonlinear Anal. Forum, 17, 107-115 (2012) · <a href="/1293.26008" class="nowrap">Zbl 1293.26008</a></td> </tr><tr> <td>[5]</td> <td class="space">Abbas, S.; Benchohra, M.; Henderson, J., Global asymptotic stability of solutions of nonlinear quadratic Volterra integral equations of fractional order, Comm. Appl. Nonlinear Anal., 19, 79-89 (2012) · <a href="/1269.26003" class="nowrap">Zbl 1269.26003</a></td> </tr><tr> <td>[6]</td> <td class="space">Abbas, S.; Benchohra, M.; N’Guérékata, GM, Advanced Fractional Differential and Integral Equations (2015), New York: Nova Science Publishers, New York · <a href="/1314.34002" class="nowrap">Zbl 1314.34002</a></td> </tr><tr> <td>[7]</td> <td class="space">Abbas, S.; Benchohra, M.; N’Guérékata, GM, Topics in Fractional Differential Equations (2012), New York: Springer, New York · <a href="/1273.35001" class="nowrap">Zbl 1273.35001</a> · <a href="https://doi.org/10.1007/978-1-4614-4036-9" class="nowrap">doi:10.1007/978-1-4614-4036-9</a></td> </tr><tr> <td>[8]</td> <td class="space">Adiguzel, RS; Aksoy, U.; Karapinar, E.; Erhan, IM, Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions, RACSAM, 115, 155 (2021) · <a href="/1490.34012" class="nowrap">Zbl 1490.34012</a> · <a href="https://doi.org/10.1007/s13398-021-01095-3" class="nowrap">doi:10.1007/s13398-021-01095-3</a></td> </tr><tr> <td>[9]</td> <td class="space">Adiguzel, RS; Aksoy, U.; Karapinar, E.; Erhan, YM, On the solution of a boundary value problem associated with a fractional differential equation, Math. Methods Appl. Sci. (2020) · <a href="/1090.83010" class="nowrap">Zbl 1090.83010</a> · <a href="https://doi.org/10.1002/mma.665" class="nowrap">doi:10.1002/mma.665</a></td> </tr><tr> <td>[10]</td> <td class="space">Adiguzel, RS; Aksoy, U.; Karapinar, E.; Erhan, YM, On the solutions of fractional differential equations via Geraghty type hybrid contractions, Appl. Comput. Math., 20, 2, 313-33 (2021) · <a href="/1541.34006" class="nowrap">Zbl 1541.34006</a></td> </tr><tr> <td>[11]</td> <td class="space">Afshari, H.; Karapınar, E., A discussion on the existence of positive solutions of the boundary value problems via $\psi $-Hilfer fractional derivative on b-metric spaces, Adv. Diff. Equ., 2020, 616 (2020) · <a href="/1486.34009" class="nowrap">Zbl 1486.34009</a> · <a href="https://doi.org/10.1186/s13662-020-03076-z" class="nowrap">doi:10.1186/s13662-020-03076-z</a></td> </tr><tr> <td>[12]</td> <td class="space">Afshari, H.; Kalantari, S.; Karapinar, E., Solution of fractional differential equations via coupled fixed point, Electron. J. Diff. Equ., 2015, 286, 1-12 (2015) · <a href="/1328.47081" class="nowrap">Zbl 1328.47081</a></td> </tr><tr> <td>[13]</td> <td class="space">Alqahtani, B.; Aydi, H.; Karapınar, E.; Rakocevic, V., A solution for Volterra fractional integral equations by hybrid contractions, Math., 7, 694 (2019) · <a href="https://doi.org/10.3390/math7080694" class="nowrap">doi:10.3390/math7080694</a></td> </tr><tr> <td>[14]</td> <td class="space">Banaś, J.; Dhage, BC, Global asymptotic stability of solutions of a functional integral equation, Nonlinear Anal., 69, 7, 1945-1952 (2008) · <a href="/1154.45005" class="nowrap">Zbl 1154.45005</a> · <a href="https://doi.org/10.1016/j.na.2007.07.038" class="nowrap">doi:10.1016/j.na.2007.07.038</a></td> </tr><tr> <td>[15]</td> <td class="space">Banaś, J.; Rzepka, B., On existence and asymptotic stability of solutions of a nonlinear integral equation, J. Math. Anal. Appl., 284, 165-173 (2003) · <a href="/1029.45003" class="nowrap">Zbl 1029.45003</a> · <a href="https://doi.org/10.1016/S0022-247X(03)00300-7" class="nowrap">doi:10.1016/S0022-247X(03)00300-7</a></td> </tr><tr> <td>[16]</td> <td class="space">Banaś, J.; Zaja̧c, T., Solvability of a functional integral equation of fractional order in the class of functions having limits at infinity, Nonlinear Anal., 71, 5491-5500 (2009) · <a href="/1181.45010" class="nowrap">Zbl 1181.45010</a> · <a href="https://doi.org/10.1016/j.na.2009.04.037" class="nowrap">doi:10.1016/j.na.2009.04.037</a></td> </tr><tr> <td>[17]</td> <td class="space">Banaś, J.; Zaja̧c, T., A new approach to the theory of functional integral equations of fractional order, J. Math. Anal. Appl., 375, 375-387 (2011) · <a href="/1210.45005" class="nowrap">Zbl 1210.45005</a> · <a href="https://doi.org/10.1016/j.jmaa.2010.09.004" class="nowrap">doi:10.1016/j.jmaa.2010.09.004</a></td> </tr><tr> <td>[18]</td> <td class="space">Burton, TA; Furumochi, T., A note on stability by Schauder’s theorem, Funkcial. Ekvac., 44, 73-82 (2001) · <a href="/1158.34329" class="nowrap">Zbl 1158.34329</a></td> </tr><tr> <td>[19]</td> <td class="space">Butzer, PL; Kilbas, AA; Trujillo, JJ, Fractional calculus in the mellin setting and Hadamard-type fractional integrals, J. Math. Anal. Appl., 269, 1-27 (2002) · <a href="/0995.26007" class="nowrap">Zbl 0995.26007</a> · <a href="https://doi.org/10.1016/S0022-247X(02)00001-X" class="nowrap">doi:10.1016/S0022-247X(02)00001-X</a></td> </tr><tr> <td>[20]</td> <td class="space">Charrier, J., Strong and weak error estimates for elliptic partial differential equations with random coefficients, SIAM J. Numer. Anal., 50, 216-246 (2012) · <a href="/1241.65011" class="nowrap">Zbl 1241.65011</a> · <a href="https://doi.org/10.1137/100800531" class="nowrap">doi:10.1137/100800531</a></td> </tr><tr> <td>[21]</td> <td class="space">Corduneanu, C., Integral equations and stability of feedback systems (1973), New York: Academic Press, New York · <a href="/0273.45001" class="nowrap">Zbl 0273.45001</a></td> </tr><tr> <td>[22]</td> <td class="space">Darwish, MA; Henderson, J.; O’Regan, D., Existence and asymptotic stability of solutions of a perturbed fractional functional integral equations with linear modification of the argument, Bull. Korean Math. Soc., 48, 3, 539-553 (2011) · <a href="/1220.45011" class="nowrap">Zbl 1220.45011</a> · <a href="https://doi.org/10.4134/BKMS.2011.48.3.539" class="nowrap">doi:10.4134/BKMS.2011.48.3.539</a></td> </tr><tr> <td>[23]</td> <td class="space">Gaul, L.; Klein, P.; Kempfle, S., Damping description involving fractional operators, Mech. Syst. Signal Process., 5, 81-88 (1991) · <a href="https://doi.org/10.1016/0888-3270(91)90016-X" class="nowrap">doi:10.1016/0888-3270(91)90016-X</a></td> </tr><tr> <td>[24]</td> <td class="space">Glockle, WG; Nonnenmacher, TF, A fractional calculus approach of selfsimilar protein dynamics, Biophys. J ., 68, 46-53 (1995) · <a href="https://doi.org/10.1016/S0006-3495(95)80157-8" class="nowrap">doi:10.1016/S0006-3495(95)80157-8</a></td> </tr><tr> <td>[25]</td> <td class="space">Han, X.; Ma, X.; Dai, G., Solutions to fourth-order random differential equations with periodic boundary conditions, Electron. J. Diff. Equ., 235, 1-9 (2012) · <a href="/1286.47047" class="nowrap">Zbl 1286.47047</a></td> </tr><tr> <td>[26]</td> <td class="space">Itoh, S., Random fixed point theorems with applications to random differential equations in Banach spaces, J. Math. Anal. Appl., 67, 261-273 (1979) · <a href="/0407.60069" class="nowrap">Zbl 0407.60069</a> · <a href="https://doi.org/10.1016/0022-247X(79)90023-4" class="nowrap">doi:10.1016/0022-247X(79)90023-4</a></td> </tr><tr> <td>[27]</td> <td class="space">Kilbas, AA; Srivastava, HM; Trujillo, JJ, Theory and applications of fractional differential equations (2006), Amsterdam: Elsevier Science B.V, Amsterdam · <a href="/1092.45003" class="nowrap">Zbl 1092.45003</a></td> </tr><tr> <td>[28]</td> <td class="space">Metzler, F.; Schick, W.; Kilian, HG; Nonnenmacher, TF, Relaxation in filled polymers: a fractional calculus approach, J. Chem. Phys., 103, 7180-7186 (1995) · <a href="https://doi.org/10.1063/1.470346" class="nowrap">doi:10.1063/1.470346</a></td> </tr><tr> <td>[29]</td> <td class="space">Miller, KS; Ross, B., An Introduction to the Fractional Calculus and Differential Equations (1993), New York: John Wiley, New York · <a href="/0789.26002" class="nowrap">Zbl 0789.26002</a></td> </tr><tr> <td>[30]</td> <td class="space">Salim, A.; Abbas, S.; Benchohra, M.; Karapinar, E., A Filippov’s theorem and topological structure of solution sets for fractional q-difference inclusions, Dynam. Syst. Appl., 31, 17-34 (2022) · <a href="https://doi.org/10.46719/dsa202231.01.02" class="nowrap">doi:10.46719/dsa202231.01.02</a></td> </tr><tr> <td>[31]</td> <td class="space">Salim, A.; Benchohra, M.; Graef, JR; Lazreg, JE, Boundary value problem for fractional generalized Hilfer-type fractional derivative with non-instantaneous impulses, Fractal Fract., 5, 1-21 (2021) · <a href="https://doi.org/10.3390/fractalfract5010001" class="nowrap">doi:10.3390/fractalfract5010001</a></td> </tr><tr> <td>[32]</td> <td class="space">Salim, A.; Benchohra, M.; Graef, JR; Lazreg, JE, Initial value problem for hybrid $\psi $-Hilfer fractional implicit differential equations, J. Fixed Point Theory Appl., 24, 14 (2022) · <a href="/1493.34037" class="nowrap">Zbl 1493.34037</a> · <a href="https://doi.org/10.1007/s11784-021-00920-x" class="nowrap">doi:10.1007/s11784-021-00920-x</a></td> </tr><tr> <td>[33]</td> <td class="space">Salim, A.; Benchohra, M.; Karapinar, E.; Lazreg, JE, Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations, Adv. Differ. Equ., 2020, 21 (2020) · <a href="/1486.34037" class="nowrap">Zbl 1486.34037</a> · <a href="https://doi.org/10.1186/s13662-020-03063-4" class="nowrap">doi:10.1186/s13662-020-03063-4</a></td> </tr><tr> <td>[34]</td> <td class="space">Salim, A.; Benchohra, M.; Lazreg, JE; Henderson, J., Nonlinear implicit generalized Hilfer-type fractional differential equations with non-instantaneous impulses in Banach spaces, Adv. Theory Nonlin. Anal. its Appl., 4, 332-348 (2020) · <a href="https://doi.org/10.31197/atnaa.825294" class="nowrap">doi:10.31197/atnaa.825294</a></td> </tr><tr> <td>[35]</td> <td class="space">Salim, A.; Benchohra, M.; Lazreg, JE; Henderson, J., On $k$-generalized $\psi $-Hilfer boundary value problems with retardation and anticipation, Adv. Theory Nonlin. Anal. its Appl., 6, 173-190 (2022) · <a href="https://doi.org/10.31197/atnaa.973992" class="nowrap">doi:10.31197/atnaa.973992</a></td> </tr><tr> <td>[36]</td> <td class="space">Salim, A.; Benchohra, M.; Lazreg, JE; Karapinar, E., On $k$-generalized $\psi $-Hilfer impulsive boundary value problem with retarded and advanced arguments, J. Math. Ext., 15, 39 (2021) · <a href="/1498.34216" class="nowrap">Zbl 1498.34216</a></td> </tr><tr> <td>[37]</td> <td class="space">Salim, A.; Benchohra, M.; Lazreg, JE; N’Guérékata, G., Boundary value problem for nonlinear implicit generalized Hilfer-type fractional differential equations with impulses, Abstr. Appl. Anal., 2021, 17 (2021) · <a href="/1482.34191" class="nowrap">Zbl 1482.34191</a> · <a href="https://doi.org/10.1155/2021/5592010" class="nowrap">doi:10.1155/2021/5592010</a></td> </tr><tr> <td>[38]</td> <td class="space">Salim, A.; Benchohra, M.; Lazreg, JE; Nieto, JJ; Zhou, Y., Nonlocal initial value problem for hybrid generalized Hilfer-type fractional implicit differential equations, Nonauton. Dyn. Syst., 8, 87-100 (2021) · <a href="/1471.34025" class="nowrap">Zbl 1471.34025</a> · <a href="https://doi.org/10.1515/msds-2020-0127" class="nowrap">doi:10.1515/msds-2020-0127</a></td> </tr><tr> <td>[39]</td> <td class="space">Samko, SG; Kilbas, AA; Marichev, OI, Fractional Integrals and Derivatives (1993), Gordon and Breach, Yverdon: Theory and Applications, Gordon and Breach, Yverdon · <a href="/0818.26003" class="nowrap">Zbl 0818.26003</a></td> </tr><tr> <td>[40]</td> <td class="space">Zielinski, DP; Voller, VR, A random walk solution for fractional diffusion equations, Int. J. Num. Meth. Heat Fluid Flow, 23, 7-22 (2013) · <a href="/1356.65015" class="nowrap">Zbl 1356.65015</a> · <a href="https://doi.org/10.1108/09615531311289088" class="nowrap">doi:10.1108/09615531311289088</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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