On Conformable Double Laplace Transform and One Dimensional Fractional Coupled Burgers’ Equation

Abstract

In the present work we introduced a new method and name it the conformable double Laplace decomposition method to solve one dimensional regular and singular conformable functional Burger’s equation. We studied the existence condition for the conformable double Laplace transform. In order to obtain the exact solution for nonlinear fractional problems, then we modified the double Laplace transform and combined it with the Adomian decomposition method. Later, we applied the new method to solve regular and singular conformable fractional coupled Burgers’ equations. Further, in order to illustrate the effectiveness of present method, we provide some examples.

Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation

“…In [15], the researchers applied the conformable double Laplace transform method and obtained the solution for the fractional partial differential equations. The conformable double Laplace decomposition method [16] has been proposed to obtain exact and approximate solutions of regular and singular one-dimensional conformable fractional coupled burgers' equations. The exact solutions of the time-fractional Burgers' equations were established by using the first integral method (see [9]).…”

Modified Modelling for Heat Like Equations within Caputo Operator

“…FPDEs are the key mathematical methods used to model many physical processes in various branches of applied science, such as physics, engineering, or other sciences. Modeling in the form of FPDEs appears in several engineering and science applications, including microelectronics, chemistry, biology, thermodynamics, chemical kinetics and other physical processes [15][16][17][18][19][20][21][22][23][24][25][26]. Different analytical and numerical methods to solve these forms of FPDEs have been published in the literature.…”

A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

“…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. Recently, the solution of fractional partial differential equations has been obtained through a double Laplace decomposition method by the authors [1][2][3]. The natural transform decomposition method has been successfully used to handle linear and nonlinear problems appearing in physical and engineering disciplines [4,5].…”