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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 954015, 9 pages
Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices
1Department of Mathematics, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran
2Department of Mathematics and Computer Sciences, Cankaya University, 06530 Ankara, Turkey
3Institute of Space Sciences, P.O. Box MG-23, 077125 Magurele-Bucharest, Romania
4Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
Received 20 February 2013; Revised 6 March 2013; Accepted 7 March 2013
Academic Editor: José Tenreiro Machado
Copyright © 2013 Mohsen Alipour and Dumitru Baleanu. 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.
- J.-H. He, “Approximate analytical solution for seepage flow with fractional derivatives in porous media,” Computer Methods in Applied Mechanics and Engineering, vol. 167, no. 1-2, pp. 57–68, 1998.
- I. Podlubny, Fractional Differential Equations, Academic Press, New York, NY, USA, 1999.
- R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
- X. Gao and J. Yu, “Synchronization of two coupled fractional-order chaotic oscillators,” Chaos, Solitons and Fractals, vol. 26, no. 1, pp. 141–145, 2005.
- J. G. Lu, “Chaotic dynamics and synchronization of fractional-order Arneodo's systems,” Chaos, Solitons & Fractals, vol. 26, no. 4, pp. 1125–1133, 2005.
- J. G. Lu and G. Chen, “A note on the fractional-order Chen system,” Chaos, Solitons & Fractals, vol. 27, no. 3, pp. 685–688, 2006.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, San Diego, Calif, USA, 2006.
- D. Baleanu, O. G. Mustafa, and R. P. Agarwal, “An existence result for a superlinear fractional differential equation,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1129–1132, 2010.
- D. Baleanu, O. G. Mustafa, and R. P. Agarwal, “On the solution set for a class of sequential fractional differential equations,” Journal of Physics A, vol. 43, no. 38, Article ID 385209, 2010.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos, World Scientific, Hackensack, NJ, USA, 2012.
- S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, and R. L. Magin, “Transient chaos in fractional Bloch equations,” Computers & Mathematics with Applications, vol. 64, no. 10, pp. 3367–3376, 2012.
- S. Momani and Z. Odibat, “Numerical approach to differential equations of fractional order,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 96–110, 2007.
- S. Momani and Z. Odibat, “Homotopy perturbation method for nonlinear partial differential equations of fractional order,” Physics Letters A, vol. 365, no. 5-6, pp. 345–350, 2007.
- S. Momani and Z. Odibat, “Numerical comparison of methods for solving linear differential equations of fractional order,” Chaos, Solitons & Fractals, vol. 31, no. 5, pp. 1248–1255, 2007.
- Z. Odibat and S. Momani, “Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order,” Chaos, Solitons & Fractals, vol. 36, no. 1, pp. 167–174, 2008.
- S. Momani and K. Al-Khaled, “Numerical solutions for systems of fractional differential equations by the decomposition method,” Applied Mathematics and Computation, vol. 162, no. 3, pp. 1351–1365, 2005.
- H. Jafari and V. Daftardar-Gejji, “Solving a system of nonlinear fractional differential equations using Adomian decomposition,” Journal of Computational and Applied Mathematics, vol. 196, no. 2, pp. 644–651, 2006.
- D. Lesnic, “The decomposition method for Cauchy advection-diffusion problems,” Computers & Mathematics with Applications, vol. 49, no. 4, pp. 525–537, 2005.
- D. Lesnic, “The decomposition method for initial value problems,” Applied Mathematics and Computation, vol. 181, no. 1, pp. 206–213, 2006.
- V. Daftardar-Gejji and H. Jafari, “Adomian decomposition: a tool for solving a system of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 301, no. 2, pp. 508–518, 2005.
- Z. M. Odibat and S. Momani, “Application of variational iteration method to nonlinear differential equations of fractional order,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 27–34, 2006.
- S. Momani and Z. Odibat, “Analytical approach to linear fractional partial differential equations arising in fluid mechanics,” Physics Letters A, vol. 355, no. 4-5, pp. 271–279, 2006.
- V. Daftardar-Gejji and H. Jafari, “An iterative method for solving nonlinear functional equations,” Journal of Mathematical Analysis and Applications, vol. 316, no. 2, pp. 753–763, 2006.
- M. Zurigat, S. Momani, Z. Odibat, and A. Alawneh, “The homotopy analysis method for handling systems of fractional differential equations,” Applied Mathematical Modelling, vol. 34, no. 1, pp. 24–35, 2010.
- V. S. Ertürk and S. Momani, “Solving systems of fractional differential equations using differential transform method,” Journal of Computational and Applied Mathematics, vol. 215, no. 1, pp. 142–151, 2008.
- M. Alipour, D. Rostamy, and D. Baleanu, “Solving multi-dimensional FOCPs with inequality constraint by BPs operational matrices,” Journal of Vibration and Control, 2012.
- D. Rostamy and K. Karimi, “Bernstein polynomials for solving fractional heat- and wave-like equations,” Fractional Calculus and Applied Analysis, vol. 15, no. 4, pp. 556–571, 2012.
- D. Rostamy, M. Alipour, H. Jafari, and D. Baleanu, “Solving multi-term orders fractional differential equations by operational matrices of BPs with convergence analysis,” Romanian Reports in Physics, vol. 65, no. 2, 2013.
- S. Momani, A. Abu Rqayiq, and D. Baleanu, “A nonstandard finite difference scheme for two-sided space-fractional partial differential equations,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 22, no. 4, Article ID 1250079, 2012.
- E. W. Cheney, Introduction to Approximation Theory, AMS Chelsea Publishing, Providence, RI, USA, 2nd edition, 1982.
- E. Kreyszig, Introduction Functional Analysis with Applications, John Wiley & Sons, New York, NY, USA, 1978.
- M. Alipour and D. Rostamy, “Bernstein polynomials for solving Abel's integral equation,” The Journal of Mathematics and Computer Science, vol. 3, no. 4, pp. 403–412, 2011.
- C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamic, Prentice-Hall, Englewood Cliffs, NJ, USA, 1988.