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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 476154, 8 pages
On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function
1Department of Mathematics, Science and Letter Faculty, Kocaeli University, Umuttepe Campus, 41380 Kocaeli, Turkey
2Ardahan University, 75000 Ardahan, Turkey
Received 22 May 2013; Revised 12 September 2013; Accepted 12 September 2013
Academic Editor: H. Srivastava
Copyright © 2013 Gülcan Özkum 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.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
- K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- S. S. Ray, K. S. Chaudhuri, and R. K. Bera, “Analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified decomposition method,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 544–552, 2006.
- K. Diethelm, “An algorithm for the numerical solution of differential equations of fractional order,” Electronic Transactions on Numerical Analysis, vol. 5, no. Mar., pp. 1–6, 1997.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific Publishing, Hackensack, NJ, USA, 2012.
- M. Alipour and D. Baleanu, “Approximate analytical solution for nonlinear system of fractional differential equations by BPs operational matrices,” Advances in Mathematical Physics, vol. 2013, Article ID 954015, 9 pages, 2013.
- G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, vol. 60 of Fundamental Theories of Physics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.
- G. Adomian, “Solutions of nonlinear P. D. E,” Applied Mathematics Letters, vol. 11, no. 3, pp. 121–123, 1998.
- K. Abbaoui and Y. Cherruault, “The decomposition method applied to the Cauchy problem,” Kybernetes, vol. 28, no. 1, pp. 68–74, 1999.
- D. Kaya and A. Yokus, “A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations,” Mathematics and Computers in Simulation, vol. 60, no. 6, pp. 507–512, 2002.
- D. A. Murio, “Time fractional IHCP with Caputo fractional derivatives,” Computers & Mathematics with Applications, vol. 56, no. 9, pp. 2371–2381, 2008.
- A. N. Bondarenko and D. S. Ivaschenko, “Numerical methods for solving inverse problems for time fractional diffusion equation with variable coefficient,” Journal of Inverse and Ill-Posed Problems, vol. 17, no. 5, pp. 419–440, 2009.
- Y. Zhang and X. Xu, “Inverse source problem for a fractional diffusion equation,” Inverse Problems, vol. 27, no. 3, Article ID 035010, 12 pages, 2011.
- M. Kirane and S. A. Malik, “Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time,” Applied Mathematics and Computation, vol. 218, no. 1, pp. 163–170, 2011.
- M. Caputo, “Linear models of dissipation whose Q is almost frequency independent—II,” Geophysical Journal International, vol. 13, no. 5, pp. 529–539, 1967.
- S. T. Mohyud-Din, A. Yıldırım, and M. Usman, “Homotopy analysis method for fractional partial differential equations,” International Journal of Physical Sciences, vol. 6, no. 1, pp. 136–145, 2011.
- G. Mittag-Leffler, “Sur la représentation analytique d'une branche uniforme d'une fonction monogène,” Acta Mathematica, vol. 29, no. 1, pp. 101–181, 1905.