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

Abstract

The conformable double Sumudu decomposition method (CDSDM) is a combination of decomposition method (DM) and a conformable double Sumudu transform. It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. Two examples are used to illustrate the method.

Wave solutions and numerical validation for the coupled reaction-advection-diffusion dynamical model in a porous medium

“…In addition, the present study affirms the findings of the available literature. More comparatively, the present study generalizes many studies, including the integer-order derivative versions of the models considered in [4,6,7]. Moreover, the employed numerical scheme which doubly serves as a semi-analytical method competes with so many methods in the literature, including [28][29][30][31][32][33][34][35][36][37]; while some known robust integration schemes that happen to contend with the two analytical methods of interest in tackling different class of evolution equations include [38][39][40][41][42][43].…”

“…The current study examines the system of coupled Burger's equations [4][5][6][7]; being one of the astonishing members of the generalized reaction-advection-diffusion dynamical model with vast applications. In doing so, two promising analytical integrations are employed; in addition to the deployment of an efficient variant of the eminent Adomian decomposition method.…”

“…Furthermore, having stated some universal nature of the governing model, and on the other hand, its application in a variety of areas of physics like fluid dynamics, environmental engineering, groundwater, and biological model; the present paper aims further to extract one of the celebrated models from the governing model that is called the system of coupled Burger's equations [4]. This model plays a vital role in modelling fluid flow problems, among others.…”

Theory and Applications of Distinctive Conformable Triple Laplace and Sumudu Transforms Decomposition Methods

“…Definition 2.3. (see [32]). Given a function f : R + ×R + ×R + → R, the conformable partial fractional derivatives (CPFDs) of order α, β and γ of the function f x α α ,…”

Modified conformable double Laplace–Sumudu approach with applications

“…Numerous mathematicians and authors have created new methods to solve conformal differential problems, including the simplest method [26], Kudryashov method [27], double Shehu transform [28], Tanh method [29,30], reliable methods [31], double Sumudu transform [32,33], conformable Laplace transform (CLT) method [34,35], conformable double Laplace transform method [36], and conformable Sumudu transform (CST) method and others [37][38][39][40][41][42][43][44].…”