Abstract
AbstractIn this paper, we study boundary value problems of fractional integro-differential equations and inclusions involving Hilfer fractional derivative. Existence and uniqueness results are obtained by using the classical fixed point theorems of Banach, Krasnosel’skiĭ, and Leray-Schauder in the single-valued case, while Martelli’s fixed point theorem, nonlinear alternative for multi-valued maps, and Covitz-Nadler fixed point theorem are used in the inclusion case. Examples illustrating the obtained results are also presented.
Highlights
In the last few decades, fractional differential equations with initial/boundary conditions have been studied by many researchers
Motivated by the research going on in this direction, in this paper, we study the existence and the uniqueness of solutions for a new class of boundary value problems of Hilfer-type fractional differential equations with nonlocal integro-multipoint boundary conditions of the form:
We present the compositional property of the Riemann-Liouville fractional integral operator with the Hilfer fractional derivative operator
Summary
In the last few decades, fractional differential equations with initial/boundary conditions have been studied by many researchers. For some more recent work on boundary value problems with Hilfer fractional derivatives we refer to the papers in [16,17,18]. Motivated by the research going on in this direction, in this paper, we study the existence and the uniqueness of solutions for a new class of boundary value problems of Hilfer-type fractional differential equations with nonlocal integro-multipoint boundary conditions of the form: HD α,βx(t) = f (t, x(t), Iδx(t)), t ∈ [a, b],. We look at the corresponding multi-valued problem by studying the existence of solutions for a new class of boundary value problems of Hilfer-type fractional differential inclusions with nonlocal integromultipoint boundary conditions of the form: HD α,βx(t) ∈ F(t, x(t), Iδx(t)), t ∈ [a, b],. The work accomplished in this paper is new and enrich the literature on boundary value problems of Hilfer-type fractional derivatives
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