Abstract
We study the existence of solutions for a new class of boundary value problems of arbitrary order fractional differential equations and inclusions, supplemented with integro-multistrip-multipoint boundary conditions. Suitable fixed point theorems are applied to prove some new existence results. The inclusion problem is discussed for convex valued as well as non-convex valued multi-valued map. Examples are also constructed to illustrate the main results. The results presented in this paper are not only new in the given configuration but also provide some interesting special cases.
Highlights
Fractional calculus, regarded as a generalization of classical calculus, deals with differential and integral operators of arbitrary non-integer orders
Influenced by application of fractional calculus, there has been shown a significant interest in the investigation of fractional differential equations and inclusions in the recent years
We prove the existence results for the inclusion boundary value problem (5) by using a variety of fixed point theorems sush as Bohnenblust–Karlin fixed point theorem, Martelli fixed point theorem, Leray–Schauder nonlinear alternative, and Covitz–Nadler fixed point theorem
Summary
Fractional calculus, regarded as a generalization of classical calculus, deals with differential and integral operators of arbitrary non-integer orders. For some recent works on fractional differential equations supplemented with multi-point and integral boundary conditions, for instance, see [12,13,14,15,16]. In a recent paper [32], the existence of solutions for an inclusions problem involving both Caputo and Hadamard fractional derivatives was studied. In [33], the authors discussed the existence and uniqueness of solutions for a Caputo type fractional differential equation cDqx(t) = f (t, x(t)), n − 1 < q ≤ n, t ∈ J := [0, 1],. The motivation of the present work is to investigate solvability criteria for fractional differential equations and inclusions of arbitrary order subject to a new kind of integro-multistrip-multipoint boundary conditions. The existence of a fixed point of the operator G will imply the existence of a solution for the problems (3) and (4)
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