Abstract
The existence of solutions of an anti-periodic boundary value problem for fractional differential inclusions of order α∈(2,3] is investigated. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.
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Ahmad, B.: Existence of solutions for fractional differential equations of order q∈(2,3] with anti-periodic boundary conditions. J. Appl. Math. Comput. doi:10.1007/s12190-009-0328-4
Ahmad, B., Otero-Espinar, V.: Existence of solutions for functional differential inclusions with antiperiodic boundary conditions. Bound. Value Probl. 2009, 625347 (2009)
Ait Dads, E., Benchohra, M., Hamani, S.: Impulsive fractional differential inclusions involving Caputo fractional derivative. Fract. Calc. Appl. Anal. 12, 15–38 (2009)
Benchohra, M., Henderson, J., Ntouyas, S.K., Ouahab, A.: Existence results for fractional order functional differential equations with infinite delay. J. Math. Anal. Appl. 338, 1340–1350 (2008)
Benchohra, M., Henderson, J., Ntouyas, S.K., Ouahab, A.: Existence results for fractional order functional differential inclusions with infinite delay and applications to control theory. Fract. Calc. Appl. Anal. 11, 35–56 (2008)
Bressan, A., Colombo, G.: Extensions and selections of maps with decomposable values. Stud. Math. 90, 69–86 (1988)
Caputo, M.: Elasticità e Dissipazione. Zanichelli, Bologna (1969)
Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions. Springer, Berlin (1977)
Cernea, A.: On the existence of solutions for fractional differential inclusions with boundary conditions. Fract. Calc. Appl. Anal. 12, 433–442 (2009)
Cernea, A.: Continuous version of Filippov’s theorem for fractional differential inclusions. Nonlinear Anal. 72, 204–208 (2010)
Cernea, A.: On the existence of solutions for nonconvex fractional hyperbolic differential inclusions. Commun. Math. Anal. 9, 109–120 (2010)
Chang, Y.K., Nieto, J.J.: Some new existence results for fractional differential inclusions with boundary conditions. Math. Comput. Model. 49, 605–609 (2009)
Chu, J., Li, M.: Positive periodic solutions of Hills equations with singular nonlinear perturbations. Nonlinear Anal. 69, 276–286 (2008)
Chu, J., Nieto, J.J.: Impulsive periodic solutions of first-order singular differential equations. Bull. Lond. Math. Soc. 40, 143–150 (2008)
Chu, J., Torres, P.J., Zhang, M.: Periodic solutions of second-order non-autonomous singular dynamical systems. J. Differ. Equ. 239, 196–212 (2007)
Covitz, H., Nadler, S.B. Jr.: Multivalued contraction mapping in generalized metric spaces. Isr. J. Math. 8, 5–11 (1970)
El-Sayed, A.M.A., Ibrahim, A.G.: Multivalued fractional differential equations of arbitrary orders. Appl. Math. Comput. 68, 15–25 (1995)
Frignon, M., Granas, A.: Théorèmes d’existence pour les inclusions différentielles sans convexité. C. R. Acad. Sci. Paris, Ser. I 310, 819–822 (1990)
Henderson, J., Ouahab, A.: Fractional functional differential inclusions with finite delay. Nonlinear Anal. 70, 2091–2105 (2009)
Jiang, D., Chu, J., Zhang, M.: Multiplicity of positive periodic solutions to superlinear repulsive singular equations. J. Differ. Equ. 211, 282–302 (2005)
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
Lasota, A., Opial, Z.: An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations. Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 13, 781–786 (1965)
Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Differential Equations. Wiley, New York (1993)
O’Regan, D.: Fixed point theory for closed multifunctions. Arch. Math. (Brno) 34, 191–197 (1998)
Ouahab, A.: Some results for fractional boundary value problem of differential inclusions. Nonlinear Anal. 69, 3871–3896 (2009)
Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
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Cernea, A. On the existence of solutions for fractional differential inclusions with anti-periodic boundary conditions. J. Appl. Math. Comput. 38, 133–143 (2012). https://doi.org/10.1007/s12190-010-0468-6
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DOI: https://doi.org/10.1007/s12190-010-0468-6