823
Views
63
CrossRef citations to date
0
Altmetric
Original Articles

A coupled method for inverse source problem of spatial fractional anomalous diffusion equations

, , &
Pages 945-956 | Received 02 Nov 2009, Accepted 16 Apr 2010, Published online: 08 Sep 2010

References

  • Chen, W, 2006. A speculative study of 2/3-order fractional Laplacian modeling of turbulence: Some thoughts and conjectures, Chaos 17 (2006), pp. 023126–023126.
  • Wang, S, Ma, ZF, and Yao, HQ, 2008. Fourier-Bessel series algorithm in fractal diffusion model for porous material, Chin. J. Comput. Phys. 25 (2008), pp. 289–295.
  • Tong, SJ, Zheng, W, and Chen, BZ, 2006. Analysis of the pollution consequences on leakage and seepage flow of poisonous liquid, Ind. Saf. Environ. Prot. 32 (2006), pp. 56–58.
  • Sun, HG, Chen, W, and Chen, Y, 2009. Variable-order fractional differential operators in anomalous diffusion modeling, Physica A, 388 (2009), pp. 4586–4592.
  • De Andrade, MR, Lenzi, EK, Evangelista, LR, Mendas, RS, and Malacarne, LC, 2005. Anomalous diffusion and fractional diffusion equation: Anisotropic media and external forces, Phys. Lett. A, 347 (2005), pp. 170–179.
  • Podlubny, I, 1999. Fractional Differential Equations. San Diego: Academic press; 1999.
  • Prakash, AO, 2004. Application of fractional derivatives in thermal analysis of disk brakes, Nonlinear Dyn. 38 (2004), pp. 191–206.
  • Depollier, C, Fellah, ZEA, and Fellah, M, 2004. Propagation of transient acoustic waves in layered porous media: Fractional equations for the scattering operators, Nonlinear Dyn. 38 (2004), pp. 181–190.
  • Cresson, J, 2010. Inverse problem of fractional calculus of variations for partial differential equations, preprint. Commun. Nonlinear Sci. Numer. Simulat. 15 (2010), pp. 987–996.
  • Battaglia, JL, Cois, O, Puigsegur, L, and Oustaloup, A, 2001. Solving an inverse heat conduction problem using a non-integer identified model, Int. J. Heat Mass Transf. 44 (2001), pp. 2671–2680.
  • Murio, DA, 2007. Stable numerical solution of a fractional-diffusion inverse heat conduction problem, Comput. Math. Appl. 53 (2007), pp. 1492–1501.
  • Murio, DA, 2008. Time fractional IHCP with Caputo fractional derivatives, Comput. Math. Appl. 56 (2008), pp. 2371–2381.
  • Sivaprasad, R, Venkatesha, S, and Manohar, CS, 2009. Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis, CMC, 298 (2009), pp. 1–29.
  • Metzler, R, and Klafter, J, 2004. The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics, J. Phys. A: Math. Gen. 37 (2004), pp. 171–208.
  • Meerschaert, MM, and Tadjeran, C, 2004. Finite difference approximations for fractional advection-dispersion flow equation, J. Comput. Appl. Math. 172 (2004), pp. 65–77.
  • Meerschaert, MM, and Tadjeran, C, 2006. Finite difference approximations for two-sided space-fractional partial differential equations, Appl. Numer. Math. 56 (2006), pp. 80–90.
  • Tadjeran, C, Meerschaert, MM, and Scheffler, H-P, 2006. A second-order accurate numerical approximation for the fractional diffusion equation, J. Comput. Phys. 213 (2006), pp. 205–213.
  • Gol’dman, NL, 2005. Determination of the right-hand side in a quasilinear parabolic equation with a final observation, J. Differ. Eqns 41 (2005), pp. 384–392.
  • Golub, GH, Hansen, PC, and Leary, DPO, 1999. Tiknonov regularization and total least square, Siam J. Matrix Anal. Appl. 21 (1999), pp. 185–194.
  • Peng, Y-M, , Research on numerical methods of the inverse problem for partial differential equations, Ph.D. diss., Xi’an University of Technology, 2004.
  • Morozov, VA, 1966. On regularization of ill-posed problems and selection of regularization parameter, J. Comput. Math. Math. Phys. 6 (1966), pp. 170–175.
  • Tikhonov, AN, and Arsenin, VY, 1977. Solution of Ill-posed Problems. New York: John Wiley & Sons; 1977.
  • Engl, HW, 1987. Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates, J. Optim. Theory Appl. 52 (1987), pp. 209–215.
  • Groesch, CW, 1984. The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind. London: Pitman Advanced Publishing Program; 1984.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.