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Difference Equ.</a> <a href="/?q=in%3A427324" title="Articles in this Issue">2019, Paper No. 119, 13 p. (2019)</a>. </div> <div class="abstract">Summary: This paper is concerned with a class of anti-periodic boundary value problems for fractional differential equations with the Riesz-Caputo derivative, which can reflected both the past and the future nonlocal memory effects. By means of new fractional Gronwall inequalities and some fixed point theorems, we obtain some existence results of solutions under the Lipschitz condition, the sublinear growth condition, the nonlinear growth condition and the comparison condition. Three examples are given to illustrate the results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7048531">Cited in <strong>11</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%3A47N20" title="MSC2020">47N20</a> </td> <td class="space"> Applications of operator theory to differential and integral equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34B15" title="MSC2020">34B15</a> </td> <td class="space"> Nonlinear boundary value problems for ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K37" title="MSC2020">34K37</a> </td> <td class="space"> Functional-differential equations with fractional derivatives </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ARiesz-Caputo+derivative">Riesz-Caputo derivative</a>; <a href="/?q=ut%3Afractional+Gronwall+inequality">fractional Gronwall inequality</a>; <a href="/?q=ut%3Afixed+point+theorem">fixed point theorem</a>; <a href="/?q=ut%3Aboundary+value+problem">boundary value problem</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <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">&times;</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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1459.34012" data-ciurl="/ci/07048531" data-biburl="/bibtex/07048531.bib" data-amsurl="/amsrefs/07048531.bib" data-xmlurl="/xml/07048531.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07048531.pdf" title="Zbl 1459.34012 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/s13662-019-2001-z" aria-label="DOI for “Anti-periodic boundary value problems with Riesz-Caputo derivative”" title="10.1186/s13662-019-2001-z">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">Li, X., Chen, F., Li, X.: Generalized anti-periodic boundary value problems of impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 18, 28-41 (2013) &middot; <a href="/1253.35207" class="nowrap">Zbl 1253.35207</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.cnsns.2012.06.014" class="nowrap">doi:10.1016/j.cnsns.2012.06.014</a></td> </tr><tr> <td>[2]</td> <td class="space">Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999) &middot; <a href="/0924.34008" class="nowrap">Zbl 0924.34008</a></td> </tr><tr> <td>[3]</td> <td class="space">Agrawal, O.P.: Fractional variational calculus in terms of Riesz fractional derivatives. J. Phys. 40, 6287-6303 (2007) &middot; <a href="/1125.26007" class="nowrap">Zbl 1125.26007</a></td> </tr><tr> <td>[4]</td> <td class="space">Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006) &middot; <a href="/1092.45003" class="nowrap">Zbl 1092.45003</a></td> </tr><tr> <td>[5]</td> <td class="space">Zhou, Y., Jiao, F., Li, J.: Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Anal. 71, 3249-3256 (2009) &middot; <a href="/1177.34084" class="nowrap">Zbl 1177.34084</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.na.2009.01.202" class="nowrap">doi:10.1016/j.na.2009.01.202</a></td> </tr><tr> <td>[6]</td> <td class="space">Zhou, Y.: Existence and uniqueness of solutions for a system of fractional differential equations. Fract. Calc. Appl. Anal. 12, 195-204 (2009) &middot; <a href="/1396.34003" class="nowrap">Zbl 1396.34003</a></td> </tr><tr> <td>[7]</td> <td class="space">Baleanu, D., Mousalou, A., Rezapour, S.: A new method for investigating approximate solutions of some fractional integro-differential equations involving the Caputo-Fabrizio derivative. Adv. Differ. Equ. 2017, 51 (2017) &middot; <a href="/1422.34219" class="nowrap">Zbl 1422.34219</a>&nbsp;&middot; <a href="https://doi.org/10.1186/s13662-017-1088-3" class="nowrap">doi:10.1186/s13662-017-1088-3</a></td> </tr><tr> <td>[8]</td> <td class="space">Baleanu, D., Mousalou, A., Rezapour, S.: On the existence of solutions for some infinite coeffcient-symmetric Caputo-Fabrizio fractional integro-differential equations. Bound. Value Probl. 2017, 145 (2017) &middot; <a href="/1377.45004" class="nowrap">Zbl 1377.45004</a>&nbsp;&middot; <a href="https://doi.org/10.1186/s13661-017-0867-9" class="nowrap">doi:10.1186/s13661-017-0867-9</a></td> </tr><tr> <td>[9]</td> <td class="space">Aydogan, S.M., Baleanu, D., Mousalou, A., et al.: On approximate solutions for two higher-order Caputo-Fabrizio fractional integro-differential equations. Adv. Differ. Equ. 2017, 221 (2017) &middot; <a href="/1422.34019" class="nowrap">Zbl 1422.34019</a>&nbsp;&middot; <a href="https://doi.org/10.1186/s13662-017-1258-3" class="nowrap">doi:10.1186/s13662-017-1258-3</a></td> </tr><tr> <td>[10]</td> <td class="space">Chen, F., Nieto, J.J., Zhou, Y.: Global attractivity for nonlinear fractional differential equations. Nonlinear Anal. 13, 287-298 (2012) &middot; <a href="/1238.34011" class="nowrap">Zbl 1238.34011</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.nonrwa.2011.07.034" class="nowrap">doi:10.1016/j.nonrwa.2011.07.034</a></td> </tr><tr> <td>[11]</td> <td class="space">Chen, F., Zhou, Y.: Existence theorem for a fractional multi-point boundary value problem. Fixed Point Theory 15, 43-58 (2014) &middot; <a href="/1312.34010" class="nowrap">Zbl 1312.34010</a></td> </tr><tr> <td>[12]</td> <td class="space">Zhou, X., Yang, F., Jiang, W.: Analytic study on linear neutral fractional differential equations. Appl. Math. Comput. 257, 295-307 (2015) &middot; <a href="/1338.34152" class="nowrap">Zbl 1338.34152</a></td> </tr><tr> <td>[13]</td> <td class="space">Xu, F.: Fractional boundary value problems with integral and anti-periodic boundary conditions. Bull. Malays. Math. Sci. Soc. 39, 571-587 (2016) &middot; <a href="/1339.34017" class="nowrap">Zbl 1339.34017</a>&nbsp;&middot; <a href="https://doi.org/10.1007/s40840-015-0126-0" class="nowrap">doi:10.1007/s40840-015-0126-0</a></td> </tr><tr> <td>[14]</td> <td class="space">Adjabi, Y., Jarad, F., Baleanu, D., Abdeljawad, T.: On Cauchy problems with Caputo Hadamard fractional derivatives. J. Comput. Anal. Appl. 21, 661-681 (2016) &middot; <a href="/1336.34010" class="nowrap">Zbl 1336.34010</a></td> </tr><tr> <td>[15]</td> <td class="space">Chen, A., Chen, Y.: Existence of solutions to anti-periodic boundary value problem for nonlinear fractional differential equations with impulses. Adv. Differ. Equ. 2011, 915689 (2011) &middot; <a href="/1219.34007" class="nowrap">Zbl 1219.34007</a></td> </tr><tr> <td>[16]</td> <td class="space">Li, Y., Chen, Y., Podlubny, I.: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Appl. 59, 1810-1821 (2010) &middot; <a href="/1189.34015" class="nowrap">Zbl 1189.34015</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.camwa.2009.08.019" class="nowrap">doi:10.1016/j.camwa.2009.08.019</a></td> </tr><tr> <td>[17]</td> <td class="space">Aguila-Camacho, N., Duarte-Mermoud, M.A., Gallegos, J.A.: Lyapunov functions for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 19, 2951-2957 (2014) &middot; <a href="/1510.34111" class="nowrap">Zbl 1510.34111</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.cnsns.2014.01.022" class="nowrap">doi:10.1016/j.cnsns.2014.01.022</a></td> </tr><tr> <td>[18]</td> <td class="space">Wang, J., Li, X.: A uniformed method to Ulam-Hyers stability for some linear fractional equations. Mediterr. J. Math. 13, 625-635 (2016) &middot; <a href="/1337.26020" class="nowrap">Zbl 1337.26020</a>&nbsp;&middot; <a href="https://doi.org/10.1007/s00009-015-0523-5" class="nowrap">doi:10.1007/s00009-015-0523-5</a></td> </tr><tr> <td>[19]</td> <td class="space">Wang, J., Li, X.: Ulam-Hyers stability of fractional Langevin equations. Appl. Math. Comput. 258, 72-83 (2015) &middot; <a href="/1338.39047" class="nowrap">Zbl 1338.39047</a></td> </tr><tr> <td>[20]</td> <td class="space">Baleanu, D., Rezapour, S., Mohammadi, H.: Some existence results on nonlinear fractional differential equations. Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci. 371, 20120144 (2013) &middot; <a href="/1342.34009" class="nowrap">Zbl 1342.34009</a>&nbsp;&middot; <a href="https://doi.org/10.1098/rsta.2012.0144" class="nowrap">doi:10.1098/rsta.2012.0144</a></td> </tr><tr> <td>[21]</td> <td class="space">Baleanu, D., Mousalou, A., Rezapour, S.: On a nonlinear fractional differential equation on partially ordered metric spaces. Adv. Differ. Equ. 2013, 83 (2013) &middot; <a href="/1380.34007" class="nowrap">Zbl 1380.34007</a>&nbsp;&middot; <a href="https://doi.org/10.1186/1687-1847-2013-83" class="nowrap">doi:10.1186/1687-1847-2013-83</a></td> </tr><tr> <td>[22]</td> <td class="space">Baleanu, D., Agarwal, R.P., Mohammadi, H., et al.: Some existence results for a nonlinear fractional differential equation on partially ordered Banach spaces. Bound. Value Probl. 2013, 112 (2013) &middot; <a href="/1301.34007" class="nowrap">Zbl 1301.34007</a>&nbsp;&middot; <a href="https://doi.org/10.1186/1687-2770-2013-112" class="nowrap">doi:10.1186/1687-2770-2013-112</a></td> </tr><tr> <td>[23]</td> <td class="space">Baleanu, D., Mousalou, A., Rezapour, S.: The existence of solutions for a nonlinear mixed problem of singular fractional differential equations. Adv. Differ. Equ. 2013, 359 (2013) &middot; <a href="/1347.34008" class="nowrap">Zbl 1347.34008</a>&nbsp;&middot; <a href="https://doi.org/10.1186/1687-1847-2013-359" class="nowrap">doi:10.1186/1687-1847-2013-359</a></td> </tr><tr> <td>[24]</td> <td class="space">Wu, G., Baleanu, D., Deng, Z., Zeng, S.: Lattice fractional diffusion equation in terms of a Riesz-Caputo difference. Physica A 438, 335-339 (2015) &middot; <a href="/1400.60130" class="nowrap">Zbl 1400.60130</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.physa.2015.06.024" class="nowrap">doi:10.1016/j.physa.2015.06.024</a></td> </tr><tr> <td>[25]</td> <td class="space">Yang, Q., Liu, F., Turner, I.: Numerical methods for fractional partial differential equations with Riesz space fractional derivatives. Appl. Math. Model. 34, 200-218 (2010) &middot; <a href="/1185.65200" class="nowrap">Zbl 1185.65200</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.apm.2009.04.006" class="nowrap">doi:10.1016/j.apm.2009.04.006</a></td> </tr><tr> <td>[26]</td> <td class="space">Wang, J., Xiang, X., Peng, Y.: Periodic solutions of semilinear impulsive periodic system on Banach space. Nonlinear Anal. 71, 1344-1353 (2009) &middot; <a href="/1238.34079" class="nowrap">Zbl 1238.34079</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.na.2009.01.139" class="nowrap">doi:10.1016/j.na.2009.01.139</a></td> </tr><tr> <td>[27]</td> <td class="space">Schaefer, H.: Uber die Methode der a priori-Schranken. Math. Ann. 129, 415-416 (1955) &middot; <a href="/0064.35703" class="nowrap">Zbl 0064.35703</a>&nbsp;&middot; <a href="https://doi.org/10.1007/BF01362380" class="nowrap">doi:10.1007/BF01362380</a></td> </tr><tr> <td>[28]</td> <td class="space">Granas, A., Guenther, R.B., Lee, J.W.: Some general existence principle in the Carathéodory theory of nonlinear differential systems. J. Math. Pures Appl. 70, 153-196 (1991) &middot; <a href="/0687.34009" class="nowrap">Zbl 0687.34009</a></td> </tr><tr> <td>[29]</td> <td class="space">Hale, J.K.: Theory of Function Differential Equations. Springer, New York (1977) &middot; <a href="/0352.34001" class="nowrap">Zbl 0352.34001</a>&nbsp;&middot; <a href="https://doi.org/10.1007/978-1-4612-9892-2" class="nowrap">doi:10.1007/978-1-4612-9892-2</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&nbsp;Open. 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