On the numerical investigations of the time-fractional modified Burgers’ equation with conformable derivative, and its stability analysis

Abstract

In this paper, we aim to introduce the cubic non-polynomial spline functions to develop a computational method for solving the fractional modified Burgers’ equation. Using the Von Neumann method, the proposed approach is shown to be conditionally stable. The proposed approach has been implemented on two test problems. The obtained results indicate that the proposed approach is a good option for solving the fractional modified Burgers’ equation. The error norms  and  have been determined to validate the accuracy and efficiency of the proposed method. The numerical solution of such kinds of models has been the key interest of researchers due to their wide range of applications in real life, optical fibers, solid-state physics, biology, plasma physics, fluid dynamics, number theory, chemical kinetics, turbulence theory, heat conduction, gas dynamics.