QUALITATIVE ANALYSIS FOR FRACTIONAL-ORDER NONLOCAL INTEGRAL-MULTIPOINT SYSTEMS VIA A GENERALIZED HILFER OPERATOR

Abstract

In this paper, we consider two types of fractional boundary value problems, one of them is an implicit type and the other will be an integro-differential type with nonlocal integral multi-point boundary conditions in the frame of generalized Hilfer fractional derivatives. The existence and uniqueness results are acquired by applying Krasnoselskii’s and Banach’s fixed point theorems. Some various numerical examples are provided to illustrate and validate our results. Moreover, we get some results in the literature as a special case of our current results.