Discontinuity, Nonlinearity, and Complexity
Analytic Solution of Time Fractional Boussinesq Equation for Groundwater Flow in Unconfined Aquifer
Discontinuity, Nonlinearity, and Complexity 8(3) (2019) 341352  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, Jaipur302017, India
$^{2}$ Department of Mathematics, Texas A&M University  Kingsville 700 University Blvd, Kingsville
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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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