Ulam–Hyers Stability of Pantograph Hadamard Fractional Stochastic Differential Equations

Abstract

In this article, we investigate the existence and uniqueness Theorem of Pantograph Hadamard fractional stochastic differential equations (PHFSDE) using the fixed-point Theorem of Banach (BFPT). According to the generalized Gronwall inequalities, we prove the stability in the sense of Ulam–Hyers (UHS) of PHFSDE. We give some examples to show the effectiveness of our results.

Keywords

• Pantograph Hadamard fractional stochastic differential equations
• existence and uniqueness
• Hyers–Ulam stability