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.
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 *