Abstract
This paper deals with the existence of solution for an impulsive Riemann–Liouville fractional neutral functional stochastic differential equation with infinite delay of order 1<beta<2 and its Hyers–Ulam stability. We prove the mild solutions for the equation using basic theorems of fractional differential equation. The existence result of the equation is obtained by Mönch’s fixed point theorem. Finally, we prove the Hyers–Ulam stability of the solution.
Highlights
Fractional differential equation [1], due to its applications in describing memory and hereditary properties of various materials and processes in natural sciences and engineering, has been widely investigated
Cui and Yan [9] studied the existence of mild solutions for neutral fractional stochastic integral differential equations with infinite delay using Sadovekii’s fixed point theorem
Sakthivel [10] studied the existence of solution to nonlinear fractional stochastic differential equations
Summary
Fractional differential equation [1], due to its applications in describing memory and hereditary properties of various materials and processes in natural sciences and engineering, has been widely investigated. M, where It2k–αk is the Riemann–Liouville fractional integral of order 2 – αk > 0 on Jk. By using Banach’s fixed point theorem, the authors developed the existence theorem for such equations.
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