Eur. Phys. J. Plus (2018) 133: 111
https://doi.org/10.1140/epjp/i2018-11961-8

Regular Article

Atangana-Batogna numerical scheme applied on a linear and non-linear fractional differential equation

Department of Mathematics, College of Science, King Saud University, P.O.Box 1142, 11989, Riyadh, Saudi Arabia

^* e-mail: balqahtani1@ksu.edu.sa

Received: 4 December 2017
Accepted: 8 January 2018
Published online: 15 March 2018

Abstract

Recently, Atangana and Batogna suggested a new numerical scheme to solve linear and non-linear equations with classical and fractional differential operators. The method can be understood as a combination of forward (or backward) approximation and the Adams-Bashforth one. This paper further presents the application of the new method to a linear and non-linear partial differential equation with integer- and non-integer-order derivative. The stability and convergence analyses are presented in detail. Some simulations are done to verify the efficiency of the new numerical scheme for solving linear and non-linear equations.