Caputo generalized proportional fractional differential equation : Analytical approach and stability results

Abstract

This paper investigates the existence, uniqueness, and stability of solutions for a novel class of Caputo generalized proportional fractional differential equations involving two distinct fractional orders. We present key properties of the generalized proportional fractional derivative and establish our main results using Schaefer’s fixed point theorem and the Banach contraction principle. Furthermore, we analyze Ulam-Hyers and generalized UlamHyers stability for the proposed problem. To illustrate the applicability of our theoretical findings, we conclude with a numerical example demonstrating these results.