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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 617010, 9 pages
New Iterative Method: An Application for Solving Fractional Physical Differential Equations
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
Received 12 September 2012; Accepted 7 March 2013
Academic Editor: Soon Y. Chung
Copyright © 2013 A. A. Hemeda. 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.
- K. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Diffrential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, London, UK, 1974.
- I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999.
- M. Amairi, M. Aoun, S. Najar, and M. N. Abdelkrim, “A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation,” Applied Mathematics and Computation, vol. 217, no. 5, pp. 2162–2168, 2010.
- J. Deng and L. Ma, “Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 6, pp. 676–680, 2010.
- E. Girejko, D. Mozyrska, and M. Wyrwas, “A sufficient condition of viability for fractional differential equations with the Caputo derivative,” Journal of Mathematical Analysis and Applications, vol. 381, no. 1, pp. 146–154, 2011.
- S. S. Ray and R. K. Bera, “Solution of an extraordinary differential equation by Adomian decomposition method,” Journal of Applied Mathematics, no. 4, pp. 331–338, 2004.
- M. Dehghan, J. Manafian, and A. Saadatmandi, “Solving nonlinear fractional partial differential equations using the homotopy analysis method,” Numerical Methods for Partial Differential Equations, vol. 26, no. 2, pp. 448–479, 2010.
- I. Hashim, O. Abdulaziz, and S. Momani, “Homotopy analysis method for fractional IVPs,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 3, pp. 674–684, 2009.
- Z. Odibat, S. Momani, and H. Xu, “A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations,” Applied Mathematical Modelling, vol. 34, no. 3, pp. 593–600, 2010.
- A. A. Hemeda, “Homotopy perturbation method for solving partial differential equations of fractional order,” International Journal of Mathematical Analysis, vol. 6, no. 49–52, pp. 2431–2448, 2012.
- A. A. Hemeda, “Homotopy perturbation method for solving systems of nonlinear coupled equations,” Applied Mathematical Sciences, vol. 6, no. 93–96, pp. 4787–4800, 2012.
- S. Esmaeili, M. Shamsi, and Y. Luchko, “Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 918–929, 2011.
- A. A. Hemeda, “Variational iteration method for solving wave equation,” Computers & Mathematics with Applications, vol. 56, no. 8, pp. 1948–1953, 2008.
- A. A. Hemeda, “Variational iteration method for solving non-linear partial differential equations,” Chaos, Solitons and Fractals, vol. 39, no. 3, pp. 1297–1303, 2009.
- A. A. Hemeda, “Variational iteration method for solving nonlinear coupled equations in 2-dimensional space in fluid mechanics,” International Journal of Contemporary Mathematical Sciences, vol. 7, no. 37–40, pp. 1839–1852, 2012.
- M. G. Sakar, F. Erdogan, and A. Yıldırım, “Variational iteration method for the time-fractional Fornberg-Whitham equation,” Computers & Mathematics with Applications, vol. 63, no. 9, pp. 1382–1388, 2012.
- E. H. Doha, A. H. Bhrawy, and S. S. Ezz-Eldien, “Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations,” Applied Mathematical Modelling, vol. 35, no. 12, pp. 5662–5672, 2011.
- E. H. Doha, A. H. Bhrawy, and S. S. Ezz-Eldien, “A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order,” Computers & Mathematics with Applications, vol. 62, no. 5, pp. 2364–2373, 2011.
- 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.
- A. A. Hemeda, “New iterative method: application to nth-order integro-differential equations,” International Mathematical Forum, vol. 7, no. 47, pp. 2317–2332, 2012.
- A. A. Hemeda, “Formulation and solution of th-order derivative fuzzy integrodifferential equation using new iterative method with a reliable algorithm,” Journal of Applied Mathematics, vol. 2012, Article ID 325473, 17 pages, 2012.
- A. Saadatmandi and M. Dehghan, “A new operational matrix for solving fractional-order differential equations,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1326–1336, 2010.
- E. H. Doha, A. H. Bhrawy, and S. S. Ezz-Eldien, “A new Jacobi operational matrix: an application for solving fractional differential equations,” Applied Mathematical Modelling, vol. 36, no. 10, pp. 4931–4943, 2012.
- B. Ghazanfari, A. G. Ghazanfari, and M. Fuladvand, “Modification of the homotopy perturbation method for numerical solution of nonlinear wave and system of nonlinear wave equations,” The Journal of Mathematics and Computer Science, vol. 3, no. 2, pp. 212–224, 2011.
- M. Caputo, “Linear methods of dissipation whose Q is almost frequency independent, part II,” Journal of the Royal Society of Medicine, vol. 13, pp. 529–539, 1967.
- Y. Cherruault, “Convergence of Adomian's method,” Kybernetes, vol. 18, no. 2, pp. 31–38, 1989.
- A. J. Jerri, Introduction to Integral Equations with Applications, Wiley-Interscience, New York, NY, USA, 2nd edition, 1999.
- S. Bhalekar and V. Daftardar-Gejji, “Convergence of the new iterative method,” International Journal of Differential Equations, vol. 2011, Article ID 989065, 10 pages, 2011.