Numerical solution of fractional partial differential equations with variable coefficients using generalized fractional-order Legendre functions

[1]  Ali H. Bhrawy,et al.  A quadrature tau method for fractional differential equations with variable coefficients , 2011, Appl. Math. Lett..

[2]  A. El-Sayed,et al.  Fractional-order diffusion-wave equation , 1996 .

[3]  A. Bhrawy,et al.  A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations , 2013 .

[4]  Saeed Kazem,et al.  Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials , 2014 .

[5]  Om Prakash Agrawal,et al.  Fractional Sturm-Liouville problem , 2013, Comput. Math. Appl..

[6]  Mehdi Dehghan,et al.  A Tau Method for the One-Dimensional Parabolic Inverse Problem Subject to Temperature Overspecification , 2006, Comput. Math. Appl..

[7]  Yiming Chen,et al.  Numerical Solution of Space-Time Fractional Convection-Diffusion Equations with Variable Coefficients Using Haar Wavelets , 2012 .

[8]  Dumitru Baleanu,et al.  A Jacobi operational matrix for solving a fuzzy linear fractional differential equation , 2013 .

[9]  A. Salimi Shamloo,et al.  Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions , 2008 .

[10]  N. Sweilam,et al.  Numerical Study for the Fractional Differential Equations Generated by Optimization Problem Using Chebyshev Collocation Method and FDM , 2013 .

[11]  Saeed Kazem,et al.  An integral operational matrix based on Jacobi polynomials for solving fractional-order differential equations , 2013 .

[12]  Shaher Momani,et al.  A generalized differential transform method for linear partial differential equations of fractional order , 2008, Appl. Math. Lett..

[13]  S. Kazem Exact Solution of Some Linear Fractional Differential Equations by Laplace Transform , 2013 .

[14]  I. P. Streltsov Application of Chebyshev and Legendre polynomials on discrete point set to function interpolation and solving Fredholm integral equations , 2000 .

[15]  Ali H. Bhrawy,et al.  The operational matrix of fractional integration for shifted Chebyshev polynomials , 2013, Appl. Math. Lett..

[16]  Ahmet Bekir,et al.  The G′G-expansion method using modified Riemann–Liouville derivative for some space-time fractional differential equations , 2014 .

[17]  Mariusz Ciesielski,et al.  Numerical solution of fractional Sturm-Liouville equation in integral form , 2014, 1405.2630.

[18]  Mehdi Dehghan,et al.  A tau approach for solution of the space fractional diffusion equation , 2011, Comput. Math. Appl..

[19]  Saeed Kazem,et al.  Fractional-order Legendre functions for solving fractional-order differential equations , 2013 .

[20]  Zhengrong Xiang,et al.  Reliable L1 control of positive switched systems with time-varying delays , 2013 .

[21]  Hongguang Sun,et al.  Finite difference Schemes for Variable-Order Time fractional Diffusion equation , 2012, Int. J. Bifurc. Chaos.

[22]  Yiming Chen,et al.  Bernstein Polynomials Method for Fractional Convection-Diffusion Equation with Variable Coefficients , 2012 .