scholarly journals ANALYSIS OF TIME-FRACTIONAL BURGERS AND DIFFUSION EQUATIONS BY USING MODIFIED q-HATM

Fractals ◽  
2021 ◽  
pp. 2240012
Author(s):  
NEHAD ALI SHAH ◽  
PRAVEEN AGARWAL ◽  
JAE DONG CHUNG ◽  
SAAD ALTHOBAITI ◽  
SAMY SAYED ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Nonlinear Partial Differential Equations ◽  
Convergent Sequence ◽  
Exact Result ◽  
Diffusion Equations ◽  
Homotopy Analysis ◽  
Linear And Nonlinear ◽  
And Diffusion

In this paper, the q-homotopy analysis transform technique is implemented to analyze the solution of fractional-order Burgers and diffusion equations with the help of Caputo operator. The results of the proposed method are shown and analyzed with the help of figures. This approach is used to determine the solution in a convergent sequence and illustrate the q-homotopy analysis transform technique solutions convergence to the exact result. Several examples showed the reliability and simplicity of the technique and highlighted the significance of this work. Therefore, the proposed method is successful in investigating other fractional-order linear and nonlinear partial differential equations.

scholarly journals An Implementation Solution for Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Nicolas Bertrand ◽  
Jocelyn Sabatier ◽  
Olivier Briat ◽  
Jean-Michel Vinassa
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Fractional Differentiation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Diffusion Equations ◽  
Electrochemical Interfaces ◽  
And Diffusion

The link between fractional differentiation and diffusion equation is used in this paper to propose a solution for the implementation of fractional diffusion equations. These equations permit us to take into account species anomalous diffusion at electrochemical interfaces, thus permitting an accurate modeling of batteries, ultracapacitors, and fuel cells. However, fractional diffusion equations are not addressed in most commercial software dedicated to partial differential equations simulation. The proposed solution is evaluated in an example.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Method ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
One Dimensional ◽  
Burger's Equation ◽  
Burger’S Equation ◽  
Sumudu Transform ◽  
Linear And Nonlinear

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.

scholarly journals Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Shailesh A. Bhanotar ◽  
Mohammed K. A. Kaabar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensions ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Linear And Nonlinear

In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This method is known as triple Laplace transform decomposition method. This method is generalized in the sense of conformable derivative. Important results and theorems concerning this method are discussed. A new algorithm is proposed to solve linear and nonlinear partial differential equations in three dimensions. Moreover, some examples are provided to verify the performance of the proposed algorithm. This method presents a wide applicability to solve nonlinear partial differential equations in the sense of conformable derivative.

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