ATANGANA-BALEANU TIME-STOCHASTIC FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS

Abstract

This study investigates the Atangana-Baleanu time-stochastic fractional neutral integro-differential equation, a complex mathematical model with broad applications in various scientific disciplines. Utilizing Banach's fixed point theory, we rigorously establish the existence and uniqueness of the mild solution to this equation. Our analysis centrally revolves around investigating the Mittag-Leffler non-singular and non-local kernel, emphasizing its crucial significance in elucidating the behavior of the equation. By integrating concepts from fractional differential equations and stochastic differential systems, we contribute to a deeper comprehension of these mathematical phenomena. Our findings not only contribute significantly to advancing theoretical understanding but also establish a solid groundwork for practical applications across various fields.

Keywords

• existence and uniqueness
• mittag-leffler non-singular and non-local kernel
• fractional differential equations