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In this manuscript, we talk over the existence of solutions of a class of hybrid Caputo-Hadamard fractional differential inclusions with Dirichlet boundary conditions. Our results are based on the Arzelá-Ascoli theorem and some suitable theorems of fixed point theory. As well, to illustrate our results, we confront the exceptional case of the fractional differential inclusions with examples.

We investigate in this manuscript the existence of solution for two fractional differential inclusions. At first we discuss the existence of solution of a class of fractional hybrid differential inclusions. To illustrate our results we present an illustrative example. We study the existence and dimension of the solution set for some fractional differential inclusions.

The goal of this paper is to investigate existence of solutions for the multiterm nonlinear fractional q-integro-differential c D α q u(t) in two modes equations and inclusions of order α ∈ (n-1, n], with non-separated boundary and initial boundary conditions where the natural number n is more than or equal to five. We consider a Carathéodory multivalued map and use Leray-Schauder and Covitz-Nadler famous fixed point theorems for finding solutions of the inclusion problems. Besides, we present results whenever the multifunctions are convex and nonconvex. Lastly, we give some examples illustrating the primary effects.

Abstract. In this paper, we investigate a Caputo fractional differential inclusion with integral boundary condition under different conditions. First, we investigate it for L 1 -Caratheodory convex-compact valued multifunction. Then, we investigate it for nonconvex-compact valued multifunction via some conditions. Also we give two examples to illustrate our results.