Some novel existence and stability results for a nonlinear implicit fractional differential equation with non-local boundary conditions

Abstract

This paper investigates nonlinear implicit fractional differential equations involving Hilfer-Katugampola fractional derivatives. Novel techniques are developed to establish the existence and uniqueness of solutions for the proposed problem using fixed-point theorems. Additionally, Hyers-Ulam stability and generalized Hyers-Ulam stability are analyzed, and an example is provided to validate the theoretical results.