A computational technique for solving the time‐fractional Fokker‐Planck equation

Abstract

In this paper, a high‐order computational scheme is constructed for the time‐fractional Fokker‐Planck (TFFP) equation. The L2−1σ$$ L2-{1}_{\sigma } $$ formula is used to approximate the fractional derivative in the model problem. The space derivatives in the resulting semi‐discrete equation are approximated by a collocation technique based on quartic B‐spline (QBS) basis functions. The method is rigorously analyzed for its convergence. Two examples are provided to show the applicability and robustness of the present method. Our results are compared with the results obtained using finite difference method (FDM) and high‐order compact finite difference method (HCFDM).

An efficient numerical scheme and its analysis for the multiterm time‐fractional convection‐diffusion‐reaction equation

“…Nayied et al [29] considered Fisher‐type nonlinear reaction‐diffusion equation and constructed a numerical scheme by utilizing collocation method based on Fibonacci wavelet. In previous works [30–32], the authors used L1 scheme for discretization of temporal fractional derivatives appearing in the governing differential equations. It should be noted that the weak singularity at $$$ t=0 $$$ was not considered in above stated papers.…”