Discussion on the existence of mild solution for fractional derivative by Mittag–Leffler kernel to fractional stochastic neutral differential inclusions

Abstract

Fractional calculus is now used to accurately depict a range of real occurrences because it can explain the “long-tail memory” phenomena that have been seen through empirical research. Standard differential equations with integer order derivatives cannot predict this influence since the future state in this case depends on a number of prior states that is equal to the maximum order of derivatives present in the differential equation. This paper is mainly focusing the existence outcomes of Atangana-Baleanu fractional stochastic systems as well as fractional neutral stochastic systems. The essential findings are developed utilizing ideals and principles of stochastic systems, multivalued map theory, fractional derivative, and fixed point approaches. We start by focusing on the existence of mild solutions for the abstract systems and we extend the analysis to the neutral system. Finally, an illustration is presented to define our primary findings.