Numerical solution of stochastic fractional integro-differential and Itô-Volterra integral equations via fractional Genocchi wavelets

In this research, a novel approach based on the fractional-order Genocchi wavelets (FGWs), inverse hyperbolic functions, and collocation technique is introduced for obtaining numerical solutions of stochastic fractional integro differential equations (SFIDEs) and Itô-Volterra integral equations (IVIEs). Initially, we utilize the Laplace trans form approach to approximate the Caputo fractional derivative. Then, the unknown solution is approximated via a combination of the FGWs and inverse hyperbolic functions. We replace this approximation and its derivatives in the resulting stochastic equation (SE). By the Gauss-Legendre quadrature rule (GLQR) and collocation method, we obtain a system of nonlinear algebraic equations. The derived algebraic system can be readily solved through application of Newton’s iterative scheme. Also, we show the convergence of the mentioned scheme. Ultimately, several test problems are examined to demonstrate the applicability and effectiveness of the suggested technique.

کلیدواژه ها:

Fractional-order Genocchi wavelets ، Fractional stochastic integro-differential equations ، Laplace transform ، Convergence analysis