Ulam type stability for mixed Hadamard and Riemann–Liouville Fractional Stochastic Differential Equations

Abstract

This study investigates the existence and Ulam–Hyers stability (UHS) results in the context of mixed Hadamard and Riemann–Liouville Fractional Stochastic Differential Equations (HRFSDEs). The primary focus is on establishing the existence and uniqueness of solutions through the application of the Banach Fixed point Theorem (BFT) coupled with standard stochastic analysis techniques. Subsequently, the UHS results for mixed HRFSDEs are explored utilizing the powerful tool of the Gronwall inequality. The theoretical findings shed light on the stability properties of the considered equations. To validate the obtained results, two numerical examples are presented, demonstrating the practical implications of the stability analysis.