Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
A second-order accurate numerical approximation for the fractional diffusion equation
Journal of Computational Physics
Mathematics and Computers in Simulation
Weighted average finite difference methods for fractional diffusion equations
Journal of Computational Physics
An approximate method for numerical solution of fractional differential equations
Signal Processing - Fractional calculus applications in signals and systems
Computers & Mathematics with Applications
SIAM Journal on Numerical Analysis
Application of Taylor series in obtaining the orthogonal operational matrix
Computers & Mathematics with Applications
A numerical technique for solving fractional optimal control problems
Computers & Mathematics with Applications
Computers & Mathematics with Applications
The Sinc-collocation method for solving the Thomas-Fermi equation
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
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Fractional differentials provide more accurate models of systems under consideration. In this paper, approximation techniques based on the shifted Legendre-tau idea are presented to solve a class of initial-boundary value problems for the fractional diffusion equations with variable coefficients on a finite domain. The fractional derivatives are described in the Caputo sense. The technique is derived by expanding the required approximate solution as the elements of shifted Legendre polynomials. Using the operational matrix of the fractional derivative the problem can be reduced to a set of linear algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous work in the literature and also it is efficient to use.