ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Analytic Solution of Time Fractional Boussinesq Equation for Groundwater Flow in Unconfined Aquifer

Discontinuity, Nonlinearity, and Complexity 8(3) (2019) 341--352 | DOI:10.5890/DNC.2019.09.009

Ritu Agarwal$^{1}$, Mahaveer Prasad Yadav$^{1}$, Ravi P. Agarwal$^{2}$

$^{1}$ Department of Mathematics, Malaviya National Institute of Technology, Jaipur-302017, India

$^{2}$ Department of Mathematics, Texas A&M University - Kingsville 700 University Blvd, Kingsville

Abstract

An approximate analytical solution to the nonlinear time fractional Boussinesq equation is presented here. Derivative with respect to time variable is replaced with Caputo fractional derivative. The Natural transform method and Adomian decomposition method are employed to obtain the solution. Some test problems are solved to show the accuracy of the proposed method. Behavior of water table head is depicted graphically for various time values.

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