A note concerning to approximate controllability of Atangana–Baleanu fractional neutral stochastic integro‐differential system with infinite delay

• Published in: Mathematical methods in the applied sciences Vol. 46; no. 9; pp. 9922 - 9941
• Main Authors: Dineshkumar, Chendrayan, Hoon Joo, Young
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 01.06.2023
• Subjects: Atangana–Baleanu derivative; Controllability; Differential calculus; Differential equations; Evolution; Fractional calculus; fractional derivatives; infinite delay; integro‐differential equation; Mathematical analysis; neutral equations; stochastic equations
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.9093

This article is primarily targeting the approximate controllability outcomes for the Atangana–Baleanu fractional neutral stochastic integro‐differential equation with infinite delay. First, by using stochastic analysis, fractional calculus, and Krasnoselskii fixed point techniques, we demonstrate the existence of mild solutions for the fractional stochastic evolution equations. Then we present a sufficient condition that ensures the approximate controllability of the stochastic evolution equations. Our findings are then applied to nonlocal conditions. At last, an example is provided to define our primary results.