The singular manifold method for a class of fractional-order diffusion equations

2022 ◽  
pp. 1-12
Author(s):  
R. Saleh ◽  
Samah M. Mabrouk ◽  
Abdul Majid Wazwaz
Keyword(s):  
Fractional Order ◽  
Diffusion Equations ◽  
Singular Manifold ◽  
Singular Manifold Method

scholarly journals Approximate analytical fractional view of convection–diffusion equations

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 897-905
Author(s):  
Hassan Khan ◽  
Saima Mustafa ◽  
Izaz Ali ◽  
Poom Kumam ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Fractional Order ◽  
Variational Iteration Method ◽  
Absolute Error ◽  
Form Solution ◽  
Diffusion Equations ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Suggested Technique ◽  
First Time ◽  
Modified Variational Iteration Method

Abstract In this article, a modified variational iteration method along with Laplace transformation is used for obtaining the solution of fractional-order nonlinear convection–diffusion equations (CDEs). The proposed technique is applied for the first time to solve fractional-order nonlinear CDEs and attain a series-form solution with the quick rate of convergence. Tabular and graphical representations are presented to confirm the reliability of the suggested technique. The solutions are calculated for fractional as well as for integer orders of the problems. The solution graphs of the solutions at various fractional derivatives are plotted. The accuracy is measured in terms of absolute error. The higher degree of accuracy is observed from the table and figures. It is further investigated that fractional solutions have the convergence behavior toward the solution at integer order. The applicability of the present technique is verified by illustrative examples. The simple and effective procedure of the current technique supports its implementation to solve other nonlinear fractional problems in different areas of applied science.

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 Numerical Solution of a Class of Time-Fractional Order Diffusion Equations in a New Reproducing Kernel Space

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaoli Zhang ◽  
Haolu Zhang ◽  
Lina Jia ◽  
Yulan Wang ◽  
Wei Zhang
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Diffusion Equations ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Reproducing Kernel Method ◽  
Reproducing Kernel Spaces ◽  
Methods Numerical

In this paper, we structure some new reproducing kernel spaces based on Jacobi polynomial and give a numerical solution of a class of time fractional order diffusion equations using piecewise reproducing kernel method (RKM). Compared with other methods, numerical results show the reliability of the present method.

Sign in / Sign up

Export Citation Format

Share Document