Analysis of Neutral Implicit Stochastic Hilfer Fractional Differential Equation Involving Lévy Noise with Retarded and Advanced Arguments

Abstract

This paper investigates the qualitative properties of the solutions for neutral implicit stochastic Hilfer fractional differential equations involving Lévy noise with retarded and advanced arguments. The existence property of the solution of the aforementioned equation is demonstrated by the Mónch condition, and the uniqueness is demonstrated by the remarkable fixed point of Banach. In addition, we examine the Hyers–Ulam (HU) stability of the presented mathematical models. To substantiate our theoretical conclusions, a real-world example is included to illustrate their practical application.

Keywords

• Hilfer fractional derivative
• stochastic
• Lévy noise
• existence
• Ulam stability