Nonlocal boundary value problems for Hilfer-type pantograph fractional differential equations and inclusions

Abstract

AbstractIn this paper, we study boundary value problems, involving the Hilfer fractional derivative, for pantograph fractional differential equations and inclusions supplemented by nonlocal integral boundary conditions. Existence and uniqueness results are obtained by using well-known fixed point theorems for single and multi-valued functions. Examples illustrating our results are also presented.