Abstract
In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.
Highlights
Fractional partial differential equations as generalizations of classical partial differential equations, and they have been proposed and applied to many applications in various fields of physical sciences and engineering such as electromagnetic, acoustics, visco-elasticity and electro-chemistry
The solution of fractional partial differential equations has been obtained through a double Laplace decomposition method by the authors [1,2,3]
Many powerful methods have been used to obtain different type solution of time-fractional Navier–Stokes equation such as the Adomian decomposition method [6], the q-homotopy analysis transform scheme [7], the modified Laplace decomposition method [8, 9], the natural homotopy perturbation method [10] and a reliable algorithm based on the new homotopy perturbation transform method [11]
Summary
Fractional partial differential equations as generalizations of classical partial differential equations, and they have been proposed and applied to many applications in various fields of physical sciences and engineering such as electromagnetic, acoustics, visco-elasticity and electro-chemistry. The solution of fractional partial differential equations has been obtained through a double Laplace decomposition method by the authors [1,2,3]. Eltayeb et al Advances in Difference Equations (2020) 2020:519 is to find the exact and approximate solution of time-fractional Navier–Stokes equations by using the double and triple Laplace Adomian decomposition methods, respectively. The triple Laplace transform for the second partial derivative with respect to x, y and t are defined by LxLyLt utt(x, y, t). M – 1 < α < m, In the theorem, one can introduce the triple Laplace transform of the partial fractional Caputo derivatives. Triple Laplace transforms of some Mittag-Leffler functions are given by LxLyLt x2 tα E1,α+1 (t).
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