Numerical study of the time-fractional partial differential equations by using quartic B-spline method

Abstract

This paper utilizes the quartic B-spline method for the numerical resolution of time-fractional partial differential equations. The fractional Caputo derivative is employed to depict anomalous diffusion processes influenced by memory effects. The proposed numerical method utilizes quartic B-spline functions for spatial discretization and employs a finite difference method to address the time-fractional derivative. Based on the Fourier method, its stability has been evaluated to demonstrate its efficacy in addressing fractional-order models. Numerical experiments, encompassing both linear and nonlinear scenarios, are performed to illustrate the method’s effectiveness and accuracy. The results obtained are compared with exact solutions and alternative numerical methods, demonstrating improved performance in convergence and computational efficiency.