Regularization for 2-D Fractional Sideways Heat Equations

REFERENCES

• J. Hadamard Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Dover, New York, 1953.
   Google Scholar
• Y. C. Hon and M. Li A Computational Method for Inverse Free Boundary Determination Problem, Int. J. Numer. Meth. Eng., vol. 73, pp. 1291–1309, 2008.
   Web of Science ®Google Scholar
• Z. Yu and J. Lin Numerical Research on the Coherent Structure in the Viscoelastic Second-Order Mixing Layers, Appl. Math. Mech., Engl. Ed., vol. 19, pp. 717–723, 1998.
   Web of Science ®Google Scholar
• T. Szabo and J. Wu A Model for Longitudinal and Shear Wave Propagation in Viscoelastic Media, J. Acoust. Soc. Am., vol. 107, Part 1, pp. 2437–2446, 2000.
   PubMedGoogle Scholar
• N. Laskin, I. Lambadaris, F. C. Harmantzis, and M. Devetsikiotis Fractional Levy Motion and Its Application to Network Traffic Modeling, Comput. Networks—Int. J. Comput. Telecom. Networking, vol. 40, pp. 363–375, 2002.
   Web of Science ®Google Scholar
• J. Bisquert Interpretation of a Fractional Diffusion Equation with Nonconserved Probability Density in Terms of Experimental Systems with Trapping or Recombination, Phys. Rev. E, vol. 72, Part 1, 2005.
   Web of Science ®Google Scholar
• R. T. Sibatov, and V. V. Uchaikin Fractional Differential Kinetics of Charge Transport in Unordered Semiconductors, Semiconductors, vol. 41, pp. 335–340, 2007.
   Web of Science ®Google Scholar
• R. Gorenflo, F. Mainardi, D. Moretti, G. Pagnini, and P. Paradisi Fractional Diffusion: Probability Distributions and Random Walk Models, Physica A—Stat. Mech. Appl., vol. 305, pp. 106–112, 2002.
   Web of Science ®Google Scholar
• R. Gorenflo, A. Vivoli, and F. Mainardi Discrete and Continuous Random Walk Models for Space-Time Fractional Diffusion, Nonlinear Dynam., vol. 38, pp. 101–116, 2004.
   Web of Science ®Google Scholar
• R. Vilela Mendes A Fractional Calculus Interpretation of the Fractional Volatility Model, Nonlinear Dynam., vol. 55, pp. 395–399, 2009.
   Web of Science ®Google Scholar
• J. V. Beck Nonlinear Estimation Applied to the Nonlinear Inverse Heat Conduction Problem, Int. J. Heat Mass Transfer, vol. 13, pp. 703–716, 1970.
   Web of Science ®Google Scholar
• L. Guo and D. Murio A Mollified Space-Marching Finite-Difference Algorithm for the Two-Dimensional Inverse Heat Conduction Problem with Slab Symmetry, Inverse Prob., vol. 7, pp. 247–259, 1991.
   Web of Science ®Google Scholar
• D. N. Hào A Mollification Method for Ill-Posed Problems, Numer. Math., vol. 68, pp. 469–506, 1994.
   Web of Science ®Google Scholar
• D. A. Murio The Mollification Method and the Numerical Solution of Ill-Posed Problems, Wiley-Interscience, New York, 1993.
   Google Scholar
• J. Cheng, J. Nakagawa, M. Yamamoto, and T. Yamazaki Uniqueness in an Inverse Problem for a One-Dimensional Fractional Diffusion Equation, Inverse Prob., vol. 25, pp. 115002, 2009.
   Web of Science ®Google Scholar
• G. H. Zheng and T. Wei Spectral Regularization Method for a Cauchy Problem of the Time Fractional Advection-Dispersion Equation, J. Comput. Appl. Math., vol. 233, pp. 2631–2640, 2010.
   Web of Science ®Google Scholar
• A. N. Bondarenko and D. S. Ivaschenko Numerical Methods for Solving Inverse Problems for Time Fractional Diffusion Equation with Variable Coefficient, J. Inverse Ill-Posed Probl., vol. 17, pp. 419–440, 2009.
   Web of Science ®Google Scholar
• D. A. Murio Stable Numerical Solution of a Fractional-Diffusion Inverse Heat Conduction Problem, Comput. Math. Appl., vol. 53, pp. 1492–1501, 2007.
   Web of Science ®Google Scholar
• Z. Qian An Optimal Modified Method for a Two-Dimensional Inverse Heat Conduction Problem, J. Math. Phys., vol. 50, 023502, 2009.
   Web of Science ®Google Scholar
• I. Podlubny Fractional Differential Equations, Academic Press, San Diego, CA, 1999.
   Google Scholar
• A. S. Carasso Determining Surface Temperatures from Interior Observations, SIAM J. Appl. Math., vol. 42, pp. 558–574, 1982.
   Web of Science ®Google Scholar
• H. E. Krogstad How to Use the MATLAB FFT2-Routines. Tech. Rep., 2004, from MATLAB Central File Exchange–File Id: 11639. http://www.mathworks.com/
   Google Scholar