Solution of the Modified Time Fractional Coupled Burgers Equations Using Laplace Adomian Decompostion Method

Abstract

In this work, a coupled system of time-fractional modified Burgers’ equations is considered. Three different fractional operators: Caputo, Caputo-Fabrizio and Atangana-Baleanu operators are implemented for the equations. Also, two different scenarios are examined for each fractional operator: when the initial conditions are u(x, y, 0) = sin(xy), v(x, y, 0) = sin(xy), and when they are u(x, y, 0) = e{−kxy}, v(x, y, 0) = e{−kxy}, where k, α are some positive constants. With the aid of computable Adomian polynomials, the solutions are obtained using Laplace Adomian decomposition method (LADM). The method does not need linearization, weak nonlinearity assumptions or perturbation theory. Simulations are also presented to support theoretical results, and the behaviour of the solutions under the three different fractional operators compared.

Analysis of the Solution of a Model of SARS-CoV-2 Variants and Its Approximation Using Two-Step Lagrange Polynomial and Euler Techniques

“…Although many methods have been developed to approximate the solutions of fractional differential equations [27][28][29], to the best of our knowledge, a comparative study of the behaviour of two-step Lagrange polynomial and fractional Euler schemes has not yet been considered. This paper aims to do so with the help of a well-formulated mathematical model for dual strains of SARS-CoV-2.…”