Two step Adams Bashforth method for time fractional Tricomi equation with non-local and non-singular Kernel

Abstract

Recently, Atangana and Baleanu (AB) introduced a new fractional differentiation concept using non-local and non-singular kernel. Later on, theoretical applications, more practical applications and new numerical methods was established for solving partial differential equations in the meaning of AB derivative. In this study, the new numerical scheme was formulated by Owolabi and Atangana [A. Atangana, K.M.Owolabi, New numerical approach for fractional differential equations. Mathematical Modelling of Natural Phenomena 13.1 (2018) 1-19.] is considered for solving fractional Tricomi equation which involves the Mittag- Leffler kernel. A novel two-step Adams-Bashforth scheme is applied for the approximation of the AB fractional derivative. Stability of the numerical scheme is examined with the help of von Neumann stability analysis and induction principle. To test the applicability and suitability of the proposed method, two notable examples are considered with numerical results presented for some fractional order values. (C) 2019 Elsevier Ltd. All rights reserved.