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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 381708, 19 pages
An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems
1School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi Selangor, Malaysia
2Department of Mathematics, Islamic Azad University, Khorasgan Branch, Isfahan, Iran
3Department of Mathematics, Imam Khomeini International University, Ghazvin 34149-16818, Iran
Received 3 June 2012; Revised 17 August 2012; Accepted 30 August 2012
Academic Editor: Dumitru Bǎleanu
Copyright © 2012 Mohammad Maleki 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 [12 citations]
The following is the list of published articles that have cited the current article.
- A. H. Bhrawy, and M. A. Alghamdi, “A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems,” Abstract and Applied Analysis, vol. 2013, pp. 1–10, 2013.
- A. H. Bhrawy, M. A. Alghamdi, and D. Baleanu, “Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method,” Abstract and Applied Analysis, vol. 2013, pp. 1–9, 2013.
- D. Baleanu, A. H. Bhrawy, and T. M. Taha, “Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems,” Abstract and Applied Analysis, vol. 2013, pp. 1–10, 2013.
- Fukang Yin, Junqiang Song, Yongwen Wu, and Lilun Zhang, “Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions,” Abstract and Applied Analysis, vol. 2013, pp. 1–13, 2013.
- A. H. Bhrawy, L. M. Assas, and M. A. Alghamdi, “Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms,” Abstract and Applied Analysis, vol. 2013, pp. 1–12, 2013.
- Mohammad Maleki, and Majid Tavassoli Kajani, “Numerical approximations for Volterra’s population growth model with fractional order via a multi-domain pseudospectral method,” Applied Mathematical Modelling, 2014.
- Mohsen Zayernouri, and George Em Karniadakis, “Fractional spectral collocation methods for linear and nonlinear variable order FPDEs,” Journal of Computational Physics, 2014.
- Arvet Pedas, and Enn Tamme, “Spline collocation for nonlinear fractional boundary value problems,” Applied Mathematics and Computation, vol. 244, pp. 502–513, 2014.
- Mohammad Maleki, Ishak Hashim, Saeid Abbasbandy, and A. Alsaedi, “Direct solution of a type of constrained fractional variational problems via an adaptive pseudospectral method,” Journal of Computational and Applied Mathematics, 2015.
- Mohsen Zayernouri, Mark Ainsworth, and George Em Karniadakis, “A unified Petrov-Galerkin spectral method for fractional PDEs,” Computer Methods In Applied Mechanics And Engineering, vol. 283, pp. 1545–1569, 2015.
- Marek Kolk, Arvet Pedas, and Enn Tamme, “Smoothing transformation and spline collocation for linear fractional boundary value problems,” Applied Mathematics and Computation, vol. 283, pp. 234–250, 2016.
- S.Yu. Reutskiy, “A novel method for solving second order fractional eigenvalue problems,” Journal of Computational and Applied Mathematics, vol. 306, pp. 133–153, 2016.