Document Zbl 1448.34003

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Difference Equ.</a> <a href="/?q=in%3A426138" title="Articles in this Issue">2018, Paper No. 328, 17 p. (2018)</a>. </div> <div class="abstract">Summary: In this article, we present some existence of weak solutions for a coupled system of implicit fractional differential equations of Hilfer-Hadamard type. Our approach is based on Mönch’s fixed point theorem associated with the technique of measure of weak noncompactness.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7007246">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34A08" title="MSC2020">34A08</a> </td> <td class="space"> Fractional ordinary differential 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><tr> <td> <a class="mono" href="/classification/?q=cc%3A35R11" title="MSC2020">35R11</a> </td> <td class="space"> Fractional partial differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34G20" title="MSC2020">34G20</a> </td> <td class="space"> Nonlinear differential equations in abstract spaces </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Acoupled+fractional+differential+system">coupled fractional differential system</a>; <a href="/?q=ut%3Aleft-sided+mixed+Pettis-Hadamard+integral+of+fractional+order">left-sided mixed Pettis-Hadamard integral of fractional order</a>; <a href="/?q=ut%3AHilfer-Hadamard+fractional+derivative">Hilfer-Hadamard fractional derivative</a>; <a href="/?q=ut%3Aweak+solution">weak solution</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 1448.34003" data-ciurl="/ci/07007246" data-biburl="/bibtex/07007246.bib" data-amsurl="/amsrefs/07007246.bib" data-xmlurl="/xml/07007246.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07007246.pdf" title="Zbl 1448.34003 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/10.1186/s13662-018-1787-4" aria-label="DOI for “Implicit coupled Hilfer-Hadamard fractional differential systems under weak topologies”" title="10.1186/s13662-018-1787-4">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Abbas, S., Benchohra, M., Bohner, M.: Weak solutions for implicit differential equations of Hilfer-Hadamard fractional derivative. Adv. Dyn. Syst. Appl. 12(1), 1-16 (2017)</td> </tr><tr> <td>[2]</td> <td class="space">Abbas, S., Benchohra, M., Graef, J.R., Henderson, J.: Implicit Fractional Differential and Integral Equations: Existence and Stability. De Gruyter, Berlin (2018) · <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., N’Guérékata, G.M.: Topics in Fractional Differential Equations. Springer, New York (2012) · <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>[4]</td> <td class="space">Abbas, S., Benchohra, M., N’Guérékata, G.M.: Advanced Fractional Differential and Integral Equations. Nova Science Publishers, New York (2015) · <a href="/1314.34002" class="nowrap">Zbl 1314.34002</a></td> </tr><tr> <td>[5]</td> <td class="space">Abbas, S., Benchohra, M., Vityuk, A.N.: On fractional order derivatives and Darboux problem for implicit differential equations. Fract. Calc. Appl. Anal. 15(2), 168-182 (2012) · <a href="/1302.35395" class="nowrap">Zbl 1302.35395</a> · <a href="https://doi.org/10.2478/s13540-012-0012-5" class="nowrap">doi:10.2478/s13540-012-0012-5</a></td> </tr><tr> <td>[6]</td> <td class="space">Akhmerov, R.R., Kamenskii, M.I., Patapov, A.S., Rodkina, A.E., Sadovskii, B.N.: Measures of Noncompactness and Condensing Operators. Birkhauser Verlag, Basel (1992) · <a href="/0748.47045" class="nowrap">Zbl 0748.47045</a> · <a href="https://doi.org/10.1007/978-3-0348-5727-7" class="nowrap">doi:10.1007/978-3-0348-5727-7</a></td> </tr><tr> <td>[7]</td> <td class="space">Alvárez, J.C.: Measure of noncompactness and fixed points of nonexpansive condensing mappings in locally convex spaces. Rev. Real. Acad. Cienc. Exact. Fis. Natur. Madrid 79, 53-66 (1985) · <a href="/0589.47054" class="nowrap">Zbl 0589.47054</a></td> </tr><tr> <td>[8]</td> <td class="space">Banaś, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Marcel Dekker, New York (1980) · <a href="/0441.47056" class="nowrap">Zbl 0441.47056</a></td> </tr><tr> <td>[9]</td> <td class="space">Benavides, T.D.: An existence theorem for implicit differential equations in a Banach space. Ann. Mat. Pura Appl. 4, 119-130 (1978) · <a href="/0418.34058" class="nowrap">Zbl 0418.34058</a> · <a href="https://doi.org/10.1007/BF02415125" class="nowrap">doi:10.1007/BF02415125</a></td> </tr><tr> <td>[10]</td> <td class="space">Benchohra, M., Graef, J., Mostefai, F.Z.: Weak solutions for boundary-value problems with nonlinear fractional differential inclusions. Nonlinear Dyn. Syst. Theory 11(3), 227-237 (2011) · <a href="/1236.34004" class="nowrap">Zbl 1236.34004</a></td> </tr><tr> <td>[11]</td> <td class="space">Benchohra, M., Henderson, J., Mostefai, F.Z.: Weak solutions for hyperbolic partial fractional differential inclusions in Banach spaces. Comput. Math. Appl. 64, 3101-3107 (2012) · <a href="/1268.35122" class="nowrap">Zbl 1268.35122</a> · <a href="https://doi.org/10.1016/j.camwa.2011.12.055" class="nowrap">doi:10.1016/j.camwa.2011.12.055</a></td> </tr><tr> <td>[12]</td> <td class="space">Benchohra, M., Henderson, J., Seba, D.: Measure of noncompactness and fractional differential equations in Banach spaces. Commun. Appl. Anal. 12(4), 419-428 (2008) · <a href="/1182.26007" class="nowrap">Zbl 1182.26007</a></td> </tr><tr> <td>[13]</td> <td class="space">Bugajewski, D., Szufla, S.: Kneser’s theorem for weak solutions of the Darboux problem in a Banach space. Nonlinear Anal. 20(2), 169-173 (1993) · <a href="/0776.34048" class="nowrap">Zbl 0776.34048</a> · <a href="https://doi.org/10.1016/0362-546X(93)90015-K" class="nowrap">doi:10.1016/0362-546X(93)90015-K</a></td> </tr><tr> <td>[14]</td> <td class="space">De Blasi, F.S.: On the property of the unit sphere in a Banach space. Bull. Math. Soc. Sci. Math. Roum. 21, 259-262 (1977) · <a href="/0365.46015" class="nowrap">Zbl 0365.46015</a></td> </tr><tr> <td>[15]</td> <td class="space">Furati, K.M., Kassim, M.D.: Non-existence of global solutions for a differential equation involving Hilfer fractional derivative. Electron. J. Differ. Equ. 2013, 235 (2013) · <a href="/1375.11024" class="nowrap">Zbl 1375.11024</a> · <a href="https://doi.org/10.1186/1687-1847-2013-235" class="nowrap">doi:10.1186/1687-1847-2013-235</a></td> </tr><tr> <td>[16]</td> <td class="space">Furati, K.M., Kassim, M.D., Tatar, N.E.: Existence and uniqueness for a problem involving Hilfer fractional derivative. Comput. Math. Appl. 64, 1616-1626 (2012) · <a href="/1268.34013" class="nowrap">Zbl 1268.34013</a> · <a href="https://doi.org/10.1016/j.camwa.2012.01.009" class="nowrap">doi:10.1016/j.camwa.2012.01.009</a></td> </tr><tr> <td>[17]</td> <td class="space">Guo, D., Lakshmikantham, V., Liu, X.: Nonlinear Integral Equations in Abstract Spaces. Kluwer Academic, Dordrecht (1996) · <a href="/0866.45004" class="nowrap">Zbl 0866.45004</a> · <a href="https://doi.org/10.1007/978-1-4613-1281-9" class="nowrap">doi:10.1007/978-1-4613-1281-9</a></td> </tr><tr> <td>[18]</td> <td class="space">Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000) · <a href="/0998.26002" class="nowrap">Zbl 0998.26002</a> · <a href="https://doi.org/10.1142/3779" class="nowrap">doi:10.1142/3779</a></td> </tr><tr> <td>[19]</td> <td class="space">Jiao, F., Zhou, Y.: Existence results for fractional boundary value problem via critical point theory. Int. J. Bifurc. Chaos 22(4), 1250086 (2012) · <a href="/1258.34015" class="nowrap">Zbl 1258.34015</a> · <a href="https://doi.org/10.1142/S0218127412500861" class="nowrap">doi:10.1142/S0218127412500861</a></td> </tr><tr> <td>[20]</td> <td class="space">Kamocki, R., Obczyński, C.: On fractional Cauchy-type problems containing Hilfer’s derivative. Electron. J. Qual. Theory Differ. Equ. 2016, 50 (2016) · <a href="/1363.26012" class="nowrap">Zbl 1363.26012</a> · <a href="https://doi.org/10.1186/s13662-015-0735-9" class="nowrap">doi:10.1186/s13662-015-0735-9</a></td> </tr><tr> <td>[21]</td> <td class="space">Kilbas, A.A.: Hadamard-type fractional calculus. J. Korean Math. Soc. 38(6), 1191-1204 (2001) · <a href="/1018.26003" class="nowrap">Zbl 1018.26003</a></td> </tr><tr> <td>[22]</td> <td class="space">Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier Science B.V., Amsterdam (2006) · <a href="/1092.45003" class="nowrap">Zbl 1092.45003</a></td> </tr><tr> <td>[23]</td> <td class="space">Li, M., Wang, J.R.: Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations. Appl. Math. Comput. 324, 254-265 (2018) · <a href="/1426.34110" class="nowrap">Zbl 1426.34110</a></td> </tr><tr> <td>[24]</td> <td class="space">Mitchell, A. R.; Smith, C.; Lakshmikantham, V. (ed.), Nonlinear equations in abstract spaces, 387-403 (1978), New York · <a href="/0452.34054" class="nowrap">Zbl 0452.34054</a></td> </tr><tr> <td>[25]</td> <td class="space">O’Regan, D.: Fixed point theory for weakly sequentially continuous mapping. Math. Comput. Model. 27(5), 1-14 (1998) · <a href="/1185.34026" class="nowrap">Zbl 1185.34026</a> · <a href="https://doi.org/10.1016/S0895-7177(98)00014-4" class="nowrap">doi:10.1016/S0895-7177(98)00014-4</a></td> </tr><tr> <td>[26]</td> <td class="space">O’Regan, D.: Weak solutions of ordinary differential equations in Banach spaces. Appl. Math. Lett. 12, 101-105 (1999) · <a href="/0933.34068" class="nowrap">Zbl 0933.34068</a> · <a href="https://doi.org/10.1016/S0893-9659(98)00133-5" class="nowrap">doi:10.1016/S0893-9659(98)00133-5</a></td> </tr><tr> <td>[27]</td> <td class="space">Pettis, B.J.: On integration in vector spaces. Trans. Am. Math. Soc. 44, 277-304 (1938) · <a href="/64.0371.02" class="nowrap">JFM 64.0371.02</a> · <a href="https://doi.org/10.1090/S0002-9947-1938-1501970-8" class="nowrap">doi:10.1090/S0002-9947-1938-1501970-8</a></td> </tr><tr> <td>[28]</td> <td class="space">Qassim, M.D., Furati, K.M., Tatar, N.-E.: On a differential equation involving Hilfer-Hadamard fractional derivative. Abstr. Appl. Anal. 2012, Article ID 391062 (2012) · <a href="/1255.34007" class="nowrap">Zbl 1255.34007</a> · <a href="https://doi.org/10.1155/2012/391062" class="nowrap">doi:10.1155/2012/391062</a></td> </tr><tr> <td>[29]</td> <td class="space">Qassim, M.D., Tatar, N.E.: Well-posedness and stability for a differential problem with Hilfer-Hadamard fractional derivative. Abstr. Appl. Anal. 2013, Article ID 605029 (2013) · <a href="/1470.34017" class="nowrap">Zbl 1470.34017</a></td> </tr><tr> <td>[30]</td> <td class="space">Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives. Theory and Applications. Gordon and Breach, Amsterdam (1987) Engl. Trans. from the Russian · <a href="/0617.26004" class="nowrap">Zbl 0617.26004</a></td> </tr><tr> <td>[31]</td> <td class="space">Tarasov, V.E.: Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media. Springer, Heidelberg (2010) · <a href="/1214.81004" class="nowrap">Zbl 1214.81004</a> · <a href="https://doi.org/10.1007/978-3-642-14003-7" class="nowrap">doi:10.1007/978-3-642-14003-7</a></td> </tr><tr> <td>[32]</td> <td class="space">Tomovski, Ž., Hilfer, R., Srivastava, H.M.: Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions. Integral Transforms Spec. Funct. 21(11), 797-814 (2010) · <a href="/1213.26011" class="nowrap">Zbl 1213.26011</a> · <a href="https://doi.org/10.1080/10652461003675737" class="nowrap">doi:10.1080/10652461003675737</a></td> </tr><tr> <td>[33]</td> <td class="space">Vityuk, A.N., Mykhailenko, A.V.: The Darboux problem for an implicit fractional-order differential equation. J. Math. Sci. 175(4), 391-401 (2011) · <a href="/1279.35092" class="nowrap">Zbl 1279.35092</a> · <a href="https://doi.org/10.1007/s10958-011-0353-3" class="nowrap">doi:10.1007/s10958-011-0353-3</a></td> </tr><tr> <td>[34]</td> <td class="space">Wang, J.R., Zhang, Y.: Nonlocal initial value problems for differential equations with Hilfer fractional derivative. Appl. Math. Comput. 266, 850-859 (2015) · <a href="/1410.34032" class="nowrap">Zbl 1410.34032</a></td> </tr><tr> <td>[35]</td> <td class="space">Zhou, Y.: Attractivity for fractional evolution equations with almost sectorial operators. Fract. Calc. Appl. Anal. 21(3), 786-800 (2018) · <a href="/1405.34012" class="nowrap">Zbl 1405.34012</a> · <a href="https://doi.org/10.1515/fca-2018-0041" class="nowrap">doi:10.1515/fca-2018-0041</a></td> </tr><tr> <td>[36]</td> <td class="space">Zhou, Y., Ahmad, B., Alsaedi, A.: Existence of nonoscillatory solutions for fractional neutral differential equations. Appl. Math. Lett. 72, 70-74 (2017) · <a href="/1373.34119" class="nowrap">Zbl 1373.34119</a> · <a href="https://doi.org/10.1016/j.aml.2017.04.016" class="nowrap">doi:10.1016/j.aml.2017.04.016</a></td> </tr><tr> <td>[37]</td> <td class="space">Zhou, Y., Shangerganesh, L., Manimaran, J., Debbouche, A.: A class of time-fractional reaction-diffusion equation with nonlocal boundary condition. Math. Methods Appl. Sci. 41, 2987-2999 (2018) · <a href="/1391.35404" class="nowrap">Zbl 1391.35404</a> · <a href="https://doi.org/10.1002/mma.4796" class="nowrap">doi:10.1002/mma.4796</a></td> </tr><tr> <td>[38]</td> <td class="space">Zhou, Y., Vijayakumar, V., Murugesu, R.: Controllability for fractional evolution inclusions without compactness. Evol. Equ. Control Theory 4, 507-524 (2015) · <a href="/1335.34096" class="nowrap">Zbl 1335.34096</a> · <a href="https://doi.org/10.3934/eect.2015.4.507" class="nowrap">doi:10.3934/eect.2015.4.507</a></td> </tr><tr> <td>[39]</td> <td class="space">Zhou, Y., Zhang, L.: Existence and multiplicity results of homoclinic solutions for fractional Hamiltonian systems. Comput. Math. Appl. 73, 1325-1345 (2017) · <a href="/1409.35232" class="nowrap">Zbl 1409.35232</a> · <a href="https://doi.org/10.1016/j.camwa.2016.04.041" class="nowrap">doi:10.1016/j.camwa.2016.04.041</a></td> </tr><tr> <td>[40]</td> <td class="space">Zhou, Y., Zhang, L., Shen, X.H.: Existence of mild solutions for fractional evolution equations. J. Integral Equ. Appl. 25, 557-586 (2013) · <a href="/1304.34013" class="nowrap">Zbl 1304.34013</a> · <a href="https://doi.org/10.1216/JIE-2013-25-4-557" class="nowrap">doi:10.1216/JIE-2013-25-4-557</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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