Abstract
The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.
Highlights
Mathematical modelling in Engineering and Scientific fields results in integral, ordinary or partial differential equations, stochastic differential equations or integro-differential equations
The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions
Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques
Summary
Mathematical modelling in Engineering and Scientific fields results in integral, ordinary or partial differential equations, stochastic differential equations or integro-differential equations. Cui and yan [23] investigated the existence results for fractional neutral stochastic integro-differential equations with infinite delay. Li et al [25] investigated the existence and Hyers-Ulam stability of random impulsive stochastic functional differential equations with finite delay. Ahmed and El. Borai [28] established the existence results of mild solutions of Hilfer fractional stochastic integro-differential equations with non-local conditions. Sayooj et al [31] considered a non-local random impulsive integro-differential system and calculated the existence, uniqueness and stability results. Let us consider a the non-local stochastic random impulsive integro-differential equation of the form dx(t) = f(t, xt)dt +.
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