Asymptotic stability of neutral stochastic functional integro-differential equations with impulses

Abstract

This paper is concerned with the existence and asymptotic stability in the p-th moment of mild solutions of nonlinear impulsive stochastic delay neutral partial functional integro-differential equations. We suppose that the linear part possesses a resolvent operator in the sense given in [8], and the nonlinear terms are assumed to be Lipschitz continuous. A fixed point approach is used to achieve the required result. An example is provided to illustrate the theory developed in this work. .

Application of flatlet oblique multiwavelets to solve the fractional stochastic integro‐differential equation using Galerkin method

“…It has been determined for some types of orthogonal, biorthogonal, and interpolate polynomials, such as flatlet oblique multiwavelets [25][26][27][28], B-spline cardinal functions [10,29], Chebyshev cardinal functions [30][31][32], Chebyshev polynomials [33], and Legendre polynomials [34] and some the other operational matrix methods [35][36][37][38][39][40][41]. In addition, recently, the creation of an operational matrix of the stochastic integral has become a popular approach for solving stochastic problems, and many researchers have tried to construct a simple and reliable operational matrix (for more details, see [7,[10][11][12][13][14][15][16][17][18][19][20][21]42]).…”

“…In recent years, there have been several methods introduced for solving SI-DEs and FSI-DEs. These methods include Bernoulli functions [7], homotopy perturbation method [8], meshless method [9], operational matrices method [10][11][12], and other methods [13][14][15][16][17][18][19][20][21]. FSI-DEs are essential for modeling and analyzing complex systems with memory and randomness.…”