A neutral stochastic differential system analysis for ABC fractional order with a constant of variations

Abstract

In this article, we explore the existence and uniqueness of mild solutions to fractional stochastic differential equations involving the ABC derivative with the Lipschitz coefficients. To do so, we extract a stochastic version of the variation of constants formula for fractional ABC differential system with the coefficients satisfying the standard Lipschitz condition. Our main goal is to establish the relationship between the integral equation and the mild solution by employing It[Formula: see text]'s isometry, martingale representation, and weighted maximum norm. Furthermore, we verify the systems Hyer–Ulam stability. We successfully illustrate the practical relevance of our theoretical results with an example.

Keywords

• Neutral fractional stochastic differential equation
• ABC derivative
• It's isometry
• Hyer–Ulam stability
• variation of constant formula
• 60H10