Title: Space time fractional Boussinesq equation with singular and non singular kernels

Authors: Ritu Agarwal; Mahaveer Prasad Yadav; Ravi P. Agarwal

Addresses: Department of Mathematics, Malaviya National Institute of Technology, Jaipur, 302017, India ' Department of Mathematics, Malaviya National Institute of Technology, Jaipur, 302017, India ' Department of Mathematics, Texas A and M University-Kingsville, Texas, 78363, USA

Abstract: Recently, many authors have found analytical and numerical solutions of fractional Boussinesq equation by applying various fractional operators with singular kernels. Motivated by recently introduced fractional operators with non-singular kernels, in this paper a comparison of the solution of linearised fractional Boussinesq equation has been made for the fractional operators Caputo (with singular kernel) and Caputo-Fabrizio (with non-singular kernel). Linearised Boussinesq equation is derived by assuming that the average thickness of saturated layer of an aquifer is constant.

Keywords: linearised Boussinesq equation; Caputo fractional derivative; Caputo Fabrizio fractional derivative; Fractional Laplacian Operator; Mittag Leffler function.

DOI: 10.1504/IJDSDE.2020.111481

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.5, pp.415 - 426

Received: 03 Nov 2018
Accepted: 22 Feb 2019

Published online: 15 Nov 2020 *

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