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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 562140, 13 pages
Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
College of Computer, National University of Defense Technology, Changsha 410073, China
Received 13 May 2013; Revised 8 September 2013; Accepted 8 September 2013
Academic Editor: Santanu Saha Ray
Copyright © 2013 Fukang Yin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citations to this Article [10 citations]
The following is the list of published articles that have cited the current article.
- Ali H. Bhrawy, Yahia A. Alhamed, Dumitru Baleanu, and Abdulrahim A. Al-Zahrani, “New spectral techniques for systems of fractional differential equations using fractional-order generalized Laguerre orthogonal functions,” Fractional Calculus and Applied Analysis, vol. 17, no. 4, pp. 1137–1157, 2014.
- A. H. Bhrawy, A. S. Alofi, and R. A. Van Gorder, “An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry,” Abstract and Applied Analysis, vol. 2014, pp. 1–9, 2014.
- A. H. Bhrawy, and M. A. Alghamdi, “A Shifted Jacobi-Gauss Collocation Scheme for Solving Fractional Neutral Functional-Differential Equations,” Advances in Mathematical Physics, vol. 2014, pp. 1–8, 2014.
- Ali H. Bhrawy, Abdulrahim AlZahrani, Dumitru Baleanu, and Yahia Alhamed, “A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014.
- B. A. Jacobs, and C. Harley, “Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations,” Abstract and Applied Analysis, vol. 2014, pp. 1–10, 2014.
- A. H. Bhrawy, M. A. Abdelkawy, and S. S. Ezz-Eldien, “Efficient Spectral Collocation Algorithm for a Two-Sided Space Fractional Boussinesq Equation with Non-local Conditions,” Mediterranean Journal of Mathematics, 2015.
- Ali H. Bhrawy, Taha M. Taha, and Jose A. Tenreiro Machado, “A review of operational matrices and spectral techniques for fractional calculus,” Nonlinear Dynamics, vol. 81, no. 3, pp. 1023–1052, 2015.
- A.H. Bhrawy, and M.A. Zaky, “A Shifted Fractional-Order Jacobi Orthogonal Functions: An Application for System of Fractional Differential Equations,” Applied Mathematical Modelling, 2015.
- Byron A. Jacobs, “High-order compact finite difference and laplace transform method for the solution of time-fractional heat equations with dirchlet and neumann boundary conditions,” Numerical Methods for Partial Differential Equations, 2015.
- P. Rahimkhani, Y. Ordokhani, and E. Babolian, “Fractional-order Bernoulli wavelets and their applications,” Applied Mathematical Modelling, 2016.