A generalized differential transform method for linear partial differential equations of fractional order

@article{Odibat2008AGD,
  title={A generalized differential transform method for linear partial differential equations of fractional order},
  author={Zaid M. Odibat and Shaher Momani},
  journal={Appl. Math. Lett.},
  year={2008},
  volume={21},
  pages={194-199}
}
  • Z. Odibat, S. Momani
  • Published 1 February 2008
  • Mathematics, Computer Science
  • Appl. Math. Lett.
Abstract In this letter we develop a new generalization of the two-dimensional differential transform method that will extend the application of the method to linear partial differential equations with space- and time-fractional derivatives. The new generalization is based on the two-dimensional differential transform method, generalized Taylor’s formula and Caputo fractional derivative. Several illustrative examples are given to demonstrate the effectiveness of the present method. The results… Expand

Tables from this paper

Differential transform method for conformable fractional partial differential equations
We expand a new generalization of the two-dimensional differential trans form method. The new generalization is based on the two-dimensional differential transform method, fractional power seriesExpand
A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula
In this article, a novel numerical method is proposed for nonlinear partial differential equations with space- and time-fractional derivatives. This method is based on the two-dimensionalExpand
Algorithms for nonlinear fractional partial differential equations: A selection of numerical methods
Fractional order partial differential equations, as generalization of classical integer order partial differential equations, are increasingly used to model problems in fluid flow, finance and otherExpand
A generalized fractional sub-equation method for fractional differential equations with variable coefficients☆
Abstract In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, thisExpand
Power Series Method for Linear Partial Differential Equations of Fractional Order
In this article, a novel numerical method is proposed for linear partial differential equations with time-fractional derivatives. This method is based on power series and generalized Taylor'sExpand
A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations
TLDR
The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative to solve the space fractional Burgers equation and the time fractional fmKdV equation. Expand
THE IMPROVED FRACTIONAL SUB-EQUATION METHOD AND ITS APPLICATIONS TO NONLINEAR FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS
The fractional derivatives in the sense of modified Riemann-Liouville derivative and the improved fractional sub-equation method are employed for constructing the exact solutions of nonlinearExpand
Lie group analysis method for two classes of fractional partial differential equations
TLDR
The infinitesimal generators general formula of n order linear fractional partial differential equation is obtained and for nonlinear fractional reaction diffusion convection equation, the properties of their infiniteimal generators are considered. Expand
The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations
An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansatz and Backlund transformation of the fractional Riccati equationExpand
A numerical approach for fractional partial differential equations by using Ritz approximation
TLDR
Ritz approximation have been employed to obtain numerical solutions of fractional partial differential equations (FPDEs) based on the Caputo fractional derivative using Mathematica7 and the coefficients of polynomial expansion are obtained. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 19 REFERENCES
Numerical comparison of methods for solving linear differential equations of fractional order
In this article, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear differential equations of fractionalExpand
Analytical approach to linear fractional partial differential equations arising in fluid mechanics
In this Letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equationsExpand
Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order
In this paper, the variational iteration method is implemented to give approximate solutions for nonlinear differential equations of fractional order. In this method the problems are initiallyExpand
Modified homotopy perturbation method : Application to quadratic Riccati differential equation of fractional order
In this paper, a modification of He’s homotopy perturbation method is presented. The new modification extends the application of the method to solve nonlinear differential equations of fractionalExpand
Solution of different type of the partial differential equation by differential transform method and Adomian's decomposition method
TLDR
Different partial differential equations are solved under the view of these methods and compared with the approximate solution and analytic solution. Expand
Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations
TLDR
Comparison of the results obtained by the homotopy perturbation method with those obtaining by the variational iteration method reveals that the present methods are very effective and convenient. Expand
An explicit and numerical solutions of the fractional KdV equation
  • S. Momani
  • Mathematics, Computer Science
  • Math. Comput. Simul.
  • 2005
TLDR
The application of Adomian decomposition method is extended to derive explicit and numerical solutions of the fractional KdV equation by replacing the first order time and space derivatives by fractional derivatives of order @a and @b with 0<@a,@b@?1. Expand
Approximate solutions for boundary value problems of time-fractional wave equation
TLDR
The decomposition method is used to construct analytical approximate solutions of time-fractional wave equation subject to specified boundary conditions and reveals that the Adomian method is very effective and convenient. Expand
Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems
In this paper, we will compare the differential transformation method DTM and Adomian decomposition method ADM to solve partial differential equations (PDEs). The definition and operations ofExpand
Analytic and approximate solutions of the space- and time-fractional telegraph equations
  • S. Momani
  • Mathematics, Computer Science
  • Appl. Math. Comput.
  • 2005
TLDR
The Adomian decomposition method is used to obtain analytic and approximate solutions of the space-and time-fractional telegraph equations and reveals that it is very effective and convenient. Expand
...
1
2
...