Numerical Solution of Time-fractional Reaction Diffusion Equation via Elzaki Transform with Residual Power Series Method

Abstract

The Elzaki transform with residual power series method is an efficient and reliable approach for solution of linear and non-linear fractional order differential equations. The major purpose of current work is to find the solution of time-fractional reaction diffusion equation by Elzaki transform with residual power series method. Elzaki transform is applied on this equation and then inverse Elzaki is taken on same equation for finding the expression of series solution. Then, assumed approximate solution is substituted on considered equation and unidentified coefficient functions are obtained by using residual function is equal to zero as well as combining its initial circumstances. At last, coefficient functions are substituted in power series form for finding finite approximate analytical solutions. The comparison between exact solution and approximate analytic solutions with different number of terms of this equation are determined and observed for reliability. This method reduces the size of computational works of solution of fractional order reaction diffusion equation. This article is anonymously gives the idea of education in Mathematics in higher studies. The nineteenth-century development of fractional derivatives and integrals, however, began with this paper, which introduced them independently. Among the scientific and engineering domains where fractional calculus is widely utilised are chemistry, physics, economics, biology, and finance. Fifteen years on, fractional calculus has gained popularity because of its proven applicability in many scientific and technical sectors.