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Original Research ARTICLE Provisionally accepted The full-text will be published soon. Notify me

Front. Phys. | doi: 10.3389/fphy.2019.00193

Fractional Approach for Equation Describing the Water Transport in Unsaturated Porous Media with Mittag-Leffler Kernel

 Jagdev Singh1*, D. G. Prakasha2 and  P. Veeresha3
  • 1JECRC University, India
  • 2Davangere University, India
  • 3Karnatak University, India

In this paper, we find the solution for fractional Richards equation describing the water transport in unsaturated porous media using q-homotopy analysis transform method (q-HATM).The proposed technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. The fixed point hypothesis considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to validate and illustrate the efficiency of the future technique, we analysed the projected model in terms of fractional order. Meanwhile, the physical behaviour of the q-HATM solutions have been captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The achieved results illuminate that, the future algorithm is easy to implement, highly methodical as well as effective and very accurate to analyse the behaviour of nonlinear differential equations of fractional order arisen in the connected areas of science and engineering.

Keywords: Laplace transform, Atangana-Baleanu derivative, Richards equation, - Homotopy analysis method, Fixed point theorem

Received: 18 Oct 2019; Accepted: 05 Nov 2019.

Copyright: © 2019 Singh, Prakasha and Veeresha. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Prof. Jagdev Singh, JECRC University, Jaipur, India, jagdevsinghrathore@gmail.com