Boundary Value Problems for Riemann–Liouville Fractional Differential Inclusions with Nonlocal Hadamard Fractional Integral Conditions

Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204. Elsevier Science B.V, Amsterdam (2006)

Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J.J.: Fractional Calculus Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos. World Scientific, Boston (2012)

Agarwal R.P., Zhou Y., He Y.: Existence of fractional neutral functional differential equations. Comput. Math. Appl. 59, 1095–1100 (2010)

Baleanu D., Mustafa O.G., Agarwal R.P.: On L p -solutions for a class of sequential fractional differential equations. Appl. Math. Comput. 218, 2074–2081 (2011)

Ahmad, B., Nieto, J.J.: Riemann–Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions. Bound. Value Probl. 36, 9 (2011)

Ahmad, B., Ntouyas, S.K., Alsaedi, A.: New existence results for nonlinear fractional differential equations with three-point integral boundary conditions. Adv. Differ. Equ., 2011, 107384 (2011)

O’Regan D., Stanek S.: Fractional boundary value problems with singularities in space variables. Nonlinear Dynam. 71, 641–652 (2013)

Ahmad, B., Ntouyas, S.K., Alsaedi, A.: A study of nonlinear fractional differential equations of arbitrary order with Riemann–Liouville type multistrip boundary conditions. Math. Probl. Eng., 2013, 320415 (2013)

Ahmad, B., Nieto, J.J.: Boundary value problems for a class of sequential integrodifferential equations of fractional order. J. Funct. Spaces Appl., 8 (2013)

Zhang L., Ahmad B., Wang G., Agarwal R.P.: Nonlinear fractional integro-differential equations on unbounded domains in a Banach space. J. Comput. Appl. Math. 249, 51–56 (2013)

Liu X., Jia M., Ge W.: Multiple solutions of a p-Laplacian model involving a fractional derivative. Adv. Differ. Equ. 2013, 126 (2013)

Hadamard J.: Essai sur l’etude des fonctions donnees par leur developpment de Taylor. J. Mat. Pure Appl. Ser. 8, 101–186 (1892)

Butzer P.L., Kilbas A.A., Trujillo J.J.: Compositions of Hadamard-type fractional integration operators and the semigroup property. J. Math. Anal. Appl. 269, 387–400 (2002)

Butzer P.L., Kilbas A.A., Trujillo J.J.: Fractional calculus in the Mellin setting and Hadamard-type fractional integrals. J. Math. Anal. Appl. 269, 1–27 (2002)

Butzer P.L., Kilbas A.A., Trujillo J.J.: Mellin transform analysis and integration by parts for Hadamard-type fractional integrals. J. Math. Anal. Appl. 270, 1–15 (2002)

Kilbas A.A.: Hadamard-type fractional calculus. J. Korean Math. Soc. 38, 1191–1204 (2001)

Kilbas A.A., Trujillo J.J.: Hadamard-type integrals as G-transforms. Integr. Transform. Spec. Funct. 14, 413–427 (2003)

Tariboon, J., Ntouyas, S.K., Sudsutad, W.: Nonlocal Hadamard fractional integral conditions for nonlinear Riemann–Liouville fractional differential equations. Bound. Value Probl. 253, 16 (2014)

Deimling, K.: Multivalued Differential Equations. Walter De Gruyter, Berlin-New York (1992)

Hu, S., Papageorgiou, N.: Handbook of Multivalued Analysis, Theory I. Kluwer, Dordrecht (1997)

Covitz H., Nadler S.B. Jr: Multivalued contraction mappings in generalized metric spaces. Israel J. Math. 8, 5–11 (1970)

Kisielewicz, M.: Differential Inclusions and Optimal Control. Kluwer, Dordrecht (1991)

Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol. 580. Springer-Verlag, Berlin-Heidelberg-New York (1977)

Granas, A., Dugundji, J.: Fixed Point Theory. Springer-Verlag, New York (2005)

Lasota A., Opial Z.: An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13, 781–786 (1965)

Bressan A., Colombo G.: Extensions and selections of maps with decomposable values. Studia Math. 90, 69–86 (1988)

Frigon, M.: Théorèmes d’existence de solutions d’inclusions différentielles. In: Granas, A., Frigon, M. (eds.) Topological Methods in Differential Equations and Inclusions, NATO ASI Series C, vol. 472, pp. 51–87. Kluwer Acad. Publ., Dordrecht (1995)