Jacobi Wavelets Based Solution of Stochastic Fractional Integro-differential Equation

Abstract

Stochastic fractional integro-differential equations have significant applications across a range of disciplines, encompassing physiology, physics, optics, climatology, biology, and more. This article introduces an innovative approach to address these equations through the presentation of a novel spectral Galerkin method based on shifted Jacobi wavelets. By employing this method, the complex problem of solving stochastic fractional integro-differential equation is converted into a set of nonlinear algebraic equations. These equations are effectively tackled using the Newton method for numerical solutions. In order to demonstrate the viability, credibility, coherence, and dependability of the proposed technique, numerical examples are given. Moreover, a comparative assessment is also conducted between the outcomes of the proposed approach and those yielded by the Chelyshkov wavelet spectral Galerkin method