Efficient Legendre spectral tau algorithm for solving the two-sided space–time Caputo fractional advection–dispersion equation

A method based on the Jacobi tau approximation for solving multi-term time–space fractional partial differential equations

(2015) A.H. Bhrawy et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Superlinearly convergent algorithms for the two-dimensional space–time Caputo–Riesz fractional diffusion equation

(2013) Minghua Chen et al.   APPLIED NUMERICAL MATHEMATICS

Fractional calculus: A survey of useful formulas

(2013) D. Valério et al.   European Physical Journal-Special Topics

Numerical solution of a class of fractional optimal control problems via the Legendre orthonormal basis combined with the operational matrix and the Gauss quadrature rule

(2013) A. Lotfi et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Two reliable wavelet methods to Fitzhugh–Nagumo (FN) and fractional FN equations

(2013) G. Hariharan et al.   JOURNAL OF MATHEMATICAL CHEMISTRY

The wavelet methods to linear and nonlinear reaction–diffusion model arising in mathematical chemistry

(2013) M. Mahalakshmi et al.   JOURNAL OF MATHEMATICAL CHEMISTRY

A new coupled wavelet-based method applied to the nonlinear reaction–diffusion equation arising in mathematical chemistry

(2013) G. Hariharan et al.   JOURNAL OF MATHEMATICAL CHEMISTRY

Numerical solution for a class of fractional convection–diffusion equations using the flatlet oblique multiwavelets

(2013) Safar Irandoust-pakchin et al.   JOURNAL OF VIBRATION AND CONTROL

Efficient generalized Laguerre-spectral methods for solving multi-term fractional differential equations on the half line

(2013) AH Bhrawy et al.   JOURNAL OF VIBRATION AND CONTROL

Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials

(2013) J.A. Rad et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Fractional-order Legendre functions for solving fractional-order differential equations

(2012) S. Kazem et al.   APPLIED MATHEMATICAL MODELLING

Homotopy perturbation method for a limit case Stefan problem governed by fractional diffusion equation

(2012) Rajeev et al.   APPLIED MATHEMATICAL MODELLING

The operational matrix of fractional integration for shifted Chebyshev polynomials

(2012) A.H. Bhrawy et al.   APPLIED MATHEMATICS LETTERS

The Sinc–Legendre collocation method for a class of fractional convection–diffusion equations with variable coefficients

(2012) Abbas Saadatmandi et al.   Communications in Nonlinear Science and Numerical Simulation

An efficient direct solver for multidimensional elliptic Robin boundary value problems using a Legendre spectral-Galerkin method

(2012) E.H. Doha et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Numerical methods and analysis for a class of fractional advection–dispersion models

(2012) F. Liu et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

A second order explicit finite difference method for the fractional advection diffusion equation

(2012) Ercília Sousa   COMPUTERS & MATHEMATICS WITH APPLICATIONS

A NONSTANDARD FINITE DIFFERENCE SCHEME FOR TWO-SIDED SPACE-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

(2012) SHAHER MOMANI et al.   INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

Quasi-Compact Finite Difference Schemes for Space Fractional Diffusion Equations

(2012) Han Zhou et al.   JOURNAL OF SCIENTIFIC COMPUTING

A method for obtaining the operational matrix of fractional Jacobi functions and applications

(2012) Amin Kayedi-Bardeh et al.   JOURNAL OF VIBRATION AND CONTROL

A new Jacobi operational matrix: An application for solving fractional differential equations

(2011) E.H. Doha et al.   APPLIED MATHEMATICAL MODELLING

A quadrature tau method for fractional differential equations with variable coefficients

(2011) A.H. Bhrawy et al.   APPLIED MATHEMATICS LETTERS

A tau approach for solution of the space fractional diffusion equation

(2011) Abbas Saadatmandi et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Multigrid method for fractional diffusion equations

(2011) Hong-Kui Pang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems

(2011) SA Yousefi et al.   JOURNAL OF VIBRATION AND CONTROL

A Legendre collocation method for fractional integro-differential equations

(2011) Abbas Saadatmandi et al.   JOURNAL OF VIBRATION AND CONTROL

A direct O(Nlog2N) finite difference method for fractional diffusion equations

(2010) Hong Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Analytical modelling of fractional advection–dispersion equation defined in a bounded space domain

(2010) A. Golbabai et al.   MATHEMATICAL AND COMPUTER MODELLING

Numerical approximations and solution techniques for the space-time Riesz–Caputo fractional advection-diffusion equation

(2010) Shujun Shen et al.   NUMERICAL ALGORITHMS

Wavelet method for a class of fractional convection-diffusion equation with variable coefficients

(2010) Yiming Chen et al.   Journal of Computational Science

Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications

(2009) Yong Zhang et al.   ADVANCES IN WATER RESOURCES

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

(2009) Q. Yang et al.   APPLIED MATHEMATICAL MODELLING

A new operational matrix for solving fractional-order differential equations

(2009) Abbas Saadatmandi et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients

(2009) Zhiqing Ding et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Application of modified decomposition method for the analytical solution of space fractional diffusion equation

(2007) S. Saha Ray et al.   APPLIED MATHEMATICS AND COMPUTATION