New techniques for the existence and stability of solutions to fractional stochastic pantograph differential equations

Abstract

In this work, we study the existence, uniqueness, and stability of fractional stochastic pantograph differential equations involving the Caputo fractional derivative. By applying a fixed-point theorem under suitable assumptions, we establish sufficient conditions for the existence and uniqueness of solutions to the proposed equations. Additionally, we prove that the solution is Hyers-Ulam stable. Our results also provide a significant generalization of existing findings in the literature. Finally, a concrete example is presented to illustrate the effectiveness of the obtained results.