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Received July 23, 2017; Accepted October 31, 2017; Published November 11, 2017
Abstract. In this paper, we study a new class of single-valued and multi-valued boundary value problems involving multiple fractional derivatives of the Caputo type and the Riemann-Liouville type fractional integral boundary conditions. The existence results for the single valued case are based on the contraction mapping principle, nonlinear alternative of the Leray-Schauder type and the Krasnoselski’s fixed point theorem, while the results for the multivalued case are obtained by applying the Leray-Schauder nonlinear alternative and the Covitz-Nadler fixed point theorem. Examples illustrating the main results are also presented. Some generalizations involving the Riemann-Liouville type integral and discrete multipoint boundary conditions are also addressed.
How to Cite this Article:
Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi, Caputo-type fractional boundary value problems for differential equations and inclusions with multiple fractional derivatives, Journal of Nonlinear Functional Analysis, Vol. 2017 (2017), Article ID 52, pp. 1-22.