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)


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.