Abstract
Abstract This paper studies the existence of solutions for a fractional differential inclusion of order q ∈ ( 2 , 3 ] with nonlinear integral boundary conditions by applying Bohnenblust-Karlin’s fixed point theorem. Some examples are presented for the illustration of the main result. MSC: 34A40, 34A12, 26A33.
Highlights
1 Introduction In this paper, we apply the Bohnenblust-Karlin fixed point theorem to prove the existence of solutions for a fractional differential inclusion with integral boundary conditions given by
Box 80203, Jeddah, 21589, Saudi Arabia. 2Department of Mathematics, University of Ioannina, Ioannina, 451 10, Greece
Summary
We apply the Bohnenblust-Karlin fixed point theorem to prove the existence of solutions for a fractional differential inclusion with integral boundary conditions given by. Where cDq denotes the Caputo fractional derivative of order q, F : [ , T] × R → R \ {∅}, g, h : [ , T] × R → R are given continuous functions and λ, μ , μ , ∈ R with λ = –. Differential inclusions of integer order (classical case) play an important role in the mathematical modeling of various situations in economics, optimal control, etc. Motivated by an extensive study of classical differential inclusions, a significant work has been established for fractional differential inclusions.
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