Numerical solution of two-dimensional fractional differential equations using Laplace transform with residual power series method

Author:

Pant Rajendra1,Arora Geeta1,Singh Brajesh Kumar2,Emadifar Homan34

Affiliation:

1. Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University , Punjab , India

2. Department of Mathematics, Babasaheb Ambedkar University , Lucknow , 226025 , India

3. Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University , Chennai-602 105 , Tamil Nadu , India

4. MEU Research Unit, Middle East University, Amman, Jordan; Department of Mathematics, Hamedan Branch, Islamic Azad University of Hamedan , Hamadan , Iran

Abstract

Abstract One of the efficient and reliable methods for resolving fractional order linear as well as non-linear differential equations is the Laplace transform with residual power series method. This approach is used in the current research to obtain the numerical solutions of the two-dimensional fractional differential equations, namely, the temporal fractional order diffusion equation and the fractional biological population equation. The unknown coefficients of the series solutions to these equations are determined using the proposed approach. The difference between exact and analytical-numerical solutions is presented for these equations in the form of errors. The advantage of the suggested method over alternative approaches is that it requires less computation to solve these two-dimensional differential equations of time-fractional order.

Publisher

Walter de Gruyter GmbH

Reference25 articles.

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