Boundary value problems of Hilfer-type fractional integro-differential equations and inclusions with nonlocal integro-multipoint boundary conditions

Abstract

In 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.

Keywords

• fractional differential equations and inclusions
• hilfer fractional derivative
• riemann-liouville fractional derivative
• caputo fractional derivative
• boundary value problems
• existence and uniqueness
• fixed point theorems
• 26a33
• 34a08
• 34b15
• 34a60