Existence and stability results to a class of fractional random implicit differential equations involving a generalized hilfer fractional derivative

Abstract

In this paper, the existence, uniqueness and stability of random implicit fractional differential equations (RIFDs) with nonlocal condition and impulsive effect involving a generalized Hilfer fractional derivative (HFD) are discussed. The arguments are discussed via Krasnoselskii's fixed point theorems, Schaefer's fixed point theorems, Banach contraction principle and Ulam type stability. Some examples are included to ensure the abstract results. © 2020 American Institute of Mathematical Sciences. All rights reserved.