Existence and Ulam stability of k-Generalized ψ-Hilfer Fractional Problem

Abstract

In this paper, we prove existence, uniqueness stability results for a class of initial value problem for fractional differential equations involving generalized ψ-Hilfer fractional derivative. The result is based on the Banach contraction mapping principle. In addition, two examples are given to illustrate our results.

Keywords

• $\psi$-Hilfer fractional derivative
• $k$-generalized $\psi$-Hilfer fractional derivative
• Cauchy-type problem
• existence and uniqueness
• generalized Gronwall inequality
• stability