Qualitative Analysis of Nonlinear Hilfer Fractional Implicit Differential Equations in a Banach Space

Abstract

This article focuses on the class of nonlinear implicit Hilfer-type fractional differential equations. By using the non-linear growth condition, we have derived the existence of at least one solution by applying Schauder’s fixed point theorem and using Lipschitz conditions, we have derived the uniqueness of the solution with the help of the Banach contraction principle. In addition, we have discussed the stability analysis by using Ulam-Hyers and Ulam-Hyers-Rassias stabilities. All results of this paper are established in a Banach space instead of R. We illustrate our results with the help of two examples. © 2023, DergiPark. All rights reserved.