Existence theory for nonlocal boundary value problems involving mixed fractional derivatives
Bashir Ahmad
King Abdulaziz University
K. Ntouyas
University of Ioannina
Ahmed Alsaedi
King Abdulaziz University
Published 2019-11-07


fractional differential equations
fractional differential inclusion
fractional derivative
boundary value problem
existence, fixed point theorems

How to Cite

Ahmad B., Ntouyas K. and Alsaedi A. (2019) “Existence theory for nonlocal boundary value problems involving mixed fractional derivatives”, Nonlinear Analysis: Modelling and Control, 24(6), pp. 937–957. doi: 10.15388/NA.2019.6.6.


In this paper, we develop the existence theory for a new kind of nonlocal three-point boundary value problems for differential equations and inclusions involving both left Caputo and right Riemann–Liouville fractional derivatives. The Banach and Krasnoselskii fixed point theorems and the Leray–Schauder nonlinear alternative are used to obtain the desired results for the singlevalued problem. The existence of solutions for the multivalued problem concerning the upper semicontinuous and Lipschitz cases is proved by applying nonlinear alternative for Kakutani maps and Covitz and Nadler fixed point theorem. Examples illustrating the main results are also presented.

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