Atangana–Baleanu time-fractional stochastic integro-differential equation

Abstract

We study the Atangana–Baleanu time-fractional stochastic integro-differential equation. Using Banach fixed point theory, we prove existence and uniqueness of mild solution. In addition, upper second moment growth estimate of the mild solution is proved and the result gives a precise exponential growth. We also give some specific examples and illustrate their growth moment bounds with graphs.

Keywords

• Atangana–Baleanu integro-differential operators
• Growth moment bounds
• Existence & uniqueness
• Mittag-Leffler
• Non-singular & non-local kernel