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International Journal of Differential Equations
Volume 2012 (2012), Article ID 975829, 12 pages
Solving Fractional-Order Logistic Equation Using a New Iterative Method
1Department of Mathematics, Shivaji University, Kolhapur 416004, India
2Department of Mathematics, University of Pune, Pune 411007, India
Received 6 May 2012; Revised 11 August 2012; Accepted 5 September 2012
Academic Editor: Om Agrawal
Copyright © 2012 Sachin Bhalekar and Varsha Daftardar-Gejji. 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.
- S. H. Strogatz, Nonlinear Dynamics and Chaos, Levant Books, Kolkata, India, 2007.
- A. M. A. El-Sayed, A. E. M. El-Mesiry, and H. A. A. El-Saka, “On the fractional-order logistic equation,” Applied Mathematics Letters, vol. 20, no. 7, pp. 817–823, 2007.
- S. Momani and R. Qaralleh, “Numerical approximations and Padé approximants for a fractional population growth model,” Applied Mathematical Modelling, vol. 31, no. 9, pp. 1907–1914, 2007.
- 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.
- 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.
- S. Bhalekar and V. Daftardar-Gejji, “New iterative method: application to partial differential equations,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 778–783, 2008.
- S. Bhalekar and V. Daftardar-Gejji, “Solving evolution equations using a new iterative method,” Numerical Methods for Partial Differential Equations, vol. 26, no. 4, pp. 906–916, 2010.
- V. Daftardar-Gejji and S. Bhalekar, “Solving fractional diffusion-wave equations using a new iterative method,” Fractional Calculus & Applied Analysis, vol. 11, no. 2, pp. 193–202, 2008.
- M. A. Noor and K. I. Noor, “Three-step iterative methods for nonlinear equations,” Applied Mathematics and Computation, vol. 183, no. 1, pp. 322–327, 2006.
- M. A. Noor, K. I. Noor, S. T. Mohyud-Din, and A. Shabbir, “An iterative method with cubic convergence for nonlinear equations,” Applied Mathematics and Computation, vol. 183, no. 2, pp. 1249–1255, 2006.
- K. I. Noor and M. A. Noor, “Iterative methods with fourth-order convergence for nonlinear equations,” Applied Mathematics and Computation, vol. 189, no. 1, pp. 221–227, 2007.
- M. A. Noor, “New iterative schemes for nonlinear equations,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 937–943, 2007.
- M. A. Noor, K. I. Noor, E. Al-Said, and M. Waseem, “Some new iterative methods for nonlinear equations,” Mathematical Problems in Engineering, vol. 2010, Article ID 198943, 12 pages, 2010.
- S. T. Mohyud-Din, A. Yildirim, and S. M. M. Hosseini, “Numerical comparison of methods for Hirota-Satsuma model,” Applications and Applied Mathematics, vol. 5, no. 10, pp. 457–466, 2010.
- S. T. Mohyud-Din, A. Yildirim, and M. M. Hosseini, “An iterative algorithm for fifth-order boundary value problems,” World Applied Sciences Journal, vol. 8, no. 5, pp. 531–535, 2010.
- M. A. Noor and S. T. Mohyud-Din, “An iterative method for solving Helmholtz equations,” Arab Journal of Mathematics and Mathematical Sciences, vol. 1, pp. 13–18, 2007.
- S. T. Mohyud-Din, A. Yildirim, and M. Hosseini, “Modified decomposition method for homogeneous and inhomogeneous advection problems,” World Applied Sciences Journal, vol. 7, pp. 168–171, 2009.
- M. Sari, A. Gunay, and G. Gurarslan, “Approximate solutions of linear and non-linear diffusion equations by using Daftardar-Gejji-Jafari's method,” International Journal of Mathematical Modelling and Numerical Optimisation, vol. 2, no. 4, pp. 376–386, 2011.
- H. Koyunbakan, “The transmutation method and Schrödinger equation with perturbed exactly solvable potential,” Journal of Computational Acoustics, vol. 17, no. 1, pp. 1–10, 2009.
- H. Koçak and A. Yıldırım, “An efficient new iterative method for finding exact solutions of nonlinear time-fractional partial differential equations,” Nonlinear Analysis: Modelling and Control, vol. 16, no. 4, pp. 403–414, 2011.
- M. Yaseen and M. Samraiz, “The modified new iterative method for solving linear and nonlinear Klein-Gordon equations,” Applied Mathematical Sciences, vol. 6, pp. 2979–2987, 2012.
- V. Srivastava and K. N. Rai, “A multi-term fractional diffusion equation for oxygen delivery through a capillary to tissues,” Mathematical and Computer Modelling, vol. 51, no. 5-6, pp. 616–624, 2010.
- M. Usman, A. Yildirim, and S. T. Mohyud-Din, “A reliable algorithm for physical problems,” International Journal of the Physical Sciences, vol. 6, no. 1, pp. 146–153, 2011.
- I. Podlubny, Fractional Differential Equations: An introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, vol. 60 of Fundamental Theories of Physics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.
- Y. Cherruault, “Convergence of Adomian's method,” Kybernetes, vol. 18, no. 2, pp. 31–38, 1989.
- J.-H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999.
- J.-H. He, “Homotopy perturbation method: a new nonlinear analytical technique,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 73–79, 2003.