A Computational Analysis of Convection-Diffusion Model with Memory using Caputo-Fabrizio Derivative and Cubic Trigonometric B-Spline Functions

This paper presents the first study on computational solutions for time-fractional partial integro-differential equations (PIDE) arising from convection-diffusion processes with memory, employing the Caputo-Fabrizio fractional derivative and the cubic trigonometric B-spline differential quadrature method. First order backward finite difference formula is used to evaluate the Caputo-Fabrizio derivative, converting the PIDE into an integro-differential equation (IDE). The cubic trigonometric B-spline-based differential quadrature method is applied to approximate the spatial derivatives, transforming the IDE into a system of algebraic equations by expressing spatial derivatives as a weighted sum of function values. The weighting coefficients are obtained using an efficient tridiagonal solver. The method is validated through three test problems, and its computational efficiency, stability, and numerical convergence are analyzed. The results are also compared with those obtained using the cubic B-spline collocation method.