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Received July 4, 2018; Accepted October 9, 2018; Published October 23, 2018
Abstract. In this paper, we study a new class of boundary value problems involving multiple fractional derivatives of Caputo type and generalized nonlocal fractional integro-differential boundary conditions. For the single-valued case, two existence results are obtained by means of nonlinear alternative of the Leray-Schauder type and the Krasnoselski’s fixed point theorem, while the uniqueness of solutions is established by applying the contraction mapping principle. For the multi-valued case, two existence results are obtained by means of the Krasnoselski’s multi-valued fixed point theorem and nonlinear alternative for contractive mappings. Examples illustrating the main results are also presented.
How to Cite this Article:
Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi, Madeaha Alghanmi, Multi-term fractional differential equations and inclusions with generalized nonlocal fractional integro-differential boundary conditions, Journal of Nonlinear Functional Analysis, Vol. 2018 (2018), Article ID 36, pp. 1-19.