@article{Algahtani2022, 
author = {Obaid Algahtani and M. A. Abdelkawy and António M. Lopes},
title = {A pseudo-spectral scheme for variable order fractional stochastic Volterra integro-differential equations},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {8},
pages = {15453-15470},
keywords = {fractional Volterra integro-differential equation, Caputo fractional derivative, spectral collocation method},
url = {https://www.sciopen.com/article/10.3934/math.2022846},
doi = {10.3934/math.2022846},
abstract = {A spectral collocation method is proposed to solve variable order fractional stochastic Volterra integro-differential equations. The new technique relies on shifted fractional order Legendre orthogonal functions outputted by Legendre polynomials. The original equations are approximated using the shifted fractional order Legendre-Gauss-Radau collocation technique. The function describing the Brownian motion is discretized by means of Lagrange interpolation. The integral components are interpolated using Legendre-Gauss-Lobatto quadrature. The approach reveals superiority over other classical techniques, especially when treating problems with non-smooth solutions.}
}