Jñānābha‎, Vol. 50 (1) (2020), 207-217

ANALYTICAL SOLUTIONS FOR TIME-FRACTIONAL CAUCHY REACTION-DIFFUSION EQUATIONS USING ITERATIVE LAPLACE TRANSFORM METHOD

By

R. K. Bairwa, Ajay Kumar and Karan Singh

Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India.

Email:dr.rajendra.maths@gmail.com, jangir.kmrajay@gmail.com,

karansinghmath@gmail.com

(Received : May 12, 2020 ; Revised: June 10, 2020)


DOI: https://doi.org/10.58250/jnanabha.2020.50120

Abstract

In the present work, the iterative Laplace transform method (ILTM) is implemented to derive approximate analytical solutions for the time-fractional Cauchy reaction-diffusion equations (CRDEs) within the Caputo fractional derivative. The proposed technique is an elegant amalgam of the Iterative method and the Laplace transform method. The ILTM produces the solution in a rapid convergent series which may lead to the solution in a closed form. The obtained analytical outcomes with the help of the proposed technique are examined graphically.

2010 Mathematics Subject Classifications: 35A20; 35A22; 34A08; 33E12

Keywords and phrases: Caputo fractional derivative,Cauchy reaction-diffusion equations,

Laplace transform, Mittag-Leffler function, Iterative Laplace transform method, fractional partial differential equations.

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