Numerical method to initial-boundary value problems for fractional partial differential equations with time-space variable coefficients

In this paper, we apply the Mickens nonstandard discretization method to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain, and thereby increase the accuracy of the solutions. We examine the case when a left-handed and a right-handed fractional spatial derivative may be present in the partial differential equation. Two numerical examples using this method are presented and compared successfully with the exact analytical solutions.

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Approximation Solution of Fractional Partial Differential Equations by Neural Networks

Advances in Numerical Analysis ◽

10.1155/2012/912810 ◽

2012 ◽

Vol 2012 ◽

pp. 1-10 ◽

Cited By ~ 4

Author(s):

Adel A. S. Almarashi

Keyword(s):

Neural Networks ◽

Partial Differential Equations ◽

Differential Equations ◽

Initial Boundary ◽

Variable Coefficients ◽

Finite Domain ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

Approximation Solution ◽

Initial Boundary Value

Neural networks with radial basis functions method are used to solve a class of initial boundary value of fractional partial differential equations with variable coefficients on a finite domain. It takes the case where a left-handed or right-handed fractional spatial derivative may be present in the partial differential equations. Convergence of this method will be discussed in the paper. A numerical example using neural networks RBF method for a two-sided fractional PDE also will be presented and compared with other methods.

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Novel solution methods for initial boundary value problems of fractional order with conformable differentiation

An International Journal of Optimization and Control Theories & Applications (IJOCTA) ◽

10.11121/ijocta.01.2018.00540 ◽

2017 ◽

Vol 8 (1) ◽

pp. 1-7 ◽

Cited By ~ 8

Author(s):

Mehmet Yavuz

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Boundary Value Problems ◽

Fractional Order ◽

Boundary Value ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

Initial Boundary Value

In this work, we develop a formulation for the approximate-analytical solution of fractional partial differential equations (PDEs) by using conformable fractional derivative. Firstly, we redefine the conformable fractional Adomian decomposition method (CFADM) and conformable fractional modified homotopy perturbation method (CFMHPM). Then, we solve some initial boundary value problems (IBVP) by using the proposed methods, which can analytically solve the fractional partial differential equations (FPDE). In order to show the efficiencies of these methods, we have compared the numerical and exact solutions of the IBVP. Also, we have found out that the proposed models are very efficient and powerful techniques in finding approximate solutions for the IBVP of fractional order in the conformable sense.

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