Numerical investigations for time-fractional nonlinear model arise in physics

Abstract

In this work, we suggest a numerical scheme to find analytically a solution of Caputo-time-fractional nonlinear model arise in physics. This model is called Belousov-Zhabotinsky (BZ) and reads asDtαu(x,t)=u(x,t)(1-u(x,t)-rv(x,t))+uxx(x,t),Dtαv(x,t)=-au(x,t)v(x,t)+vxx(x,t),where 0<α⩽1,0<t<R<1. Also, a≠1 and r are positive parameters. A modified version of generalized Taylor power series method will be used in this work. Graphical justifications on the reliability of the proposed method are provided. Finally, the effects of the fractional order on the solution of Belousov-Zhabotinsky model is also discussed. MSC(2010): 26A33, 35F25, 35C10, Keywords: Time-fractional Belousov-Zhabotinsky equation, Approximate solutions, Generalized Taylor series