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A NOVEL SERIES METHOD FOR FRACTIONAL DIFFUSION EQUATION WITHIN CAPUTO FRACTIONAL DERIVATIVE

ABSTRACT
In this paper, we suggest the series expansion method for finding the series solution for the time-fractional diffusion equation involving Caputo fractional derivative.
KEYWORDS
PAPER SUBMITTED: 2016-01-17
PAPER REVISED: 2016-02-23
PAPER ACCEPTED: 2016-03-26
PUBLISHED ONLINE: 2016-09-24
DOI REFERENCE: https://doi.org/10.2298/TSCI16S3695Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S695 - S699]
REFERENCES
  1. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2015
  2. Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006
  3. Podlubny, I., Fractional Differential Equations, Academic Press, London, New York, USA, 1999
  4. Sabatier, J., et al., Advances in Fractional Calculus, Springer, New York, USA, 2007
  5. Ortigueira, M. D., Fractional Calculus for Scientists and Engineers, Springer, New York, USA, 2011
  6. Diethelm, K., The Analysis of Fractional Differential Equations: An Application-oriented Exposition Using Differential Operators of Caputo Type, Springer, New York, USA, 2010
  7. Chen, W., et al., Anomalous Diffusion Modeling by Fractal and Fractional Derivatives, Computers & Mathematics with Applications, 59 (2010), 5, pp. 1754-1758
  8. Khader, M. M., On the Numerical Solutions for the Fractional Diffusion Equation, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 6, pp. 2535-2542
  9. Li, X., et al., A Space-Time Spectral Method for the Time Fractional Diffusion Equation, SIAM Journal on Numerical Analysis, 47 (2009), 3, pp. 2108-2131
  10. Liu, F., et al., A Fractional-Order Implicit Difference Approximation for the Space-Time Fractional Diffusion Equation, ANZIAM Journal, 47 (2006), June, pp. 48-68
  11. Dehghan, M., et al., Legendre Spectral Element Method for Solving Time Fractional Modified Anomalous Sub-Diffusion Equation, Applied Mathematical Modelling, 40 (2016), 5-6, pp. 3635-3654
  12. Yang, X. J., et al., Local Fractional Homotopy Perturbation Method for Solving Fractal Partial Differential Equations Arising in Mathematical Physics, Romanian Reports in Physics, 67 (2015), 3, pp. 752-761
  13. Yang, X. J., et al., A New Numerical Technique for Solving the Local Fractional Diffusion Equation: Two-Dimensional Extended Differential Transform Approach, Applied Mathematics and Computation, 274 (2016), Feb., pp. 143-151
  14. Yang, X. J., et al., Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets, Applied Mathematical Letters, 47 (2015), Sep., pp. 54-60
  15. Yan, S. P., Local Fractional Laplace Series Expansion Method for Diffusion Equation Arising in Fractal Heat Transfer, Thermal Science, 19 (2015), Suppl. 1, pp. S131-S135
  16. Yang, A. M., et al., Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets, Abstract Applied Analysis, 2013 (2013), ID 351057
  17. Zhao, Y., et al., Approximation Solutions for Local Fractional Schroedinger Equation in the One- Dimensional Cantorian System, Advances in Mathematical Physics, 2013 (2013), ID 291386
  18. Li, Z. B., et al, Fractional Series Expansion Method for Fractional Differential Equations, International Journal of Numerical Methods for Heat & Fluid Flow, 25 (2015), 7, pp. 1525-1530

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence