THERMAL SCIENCE

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Yun Qiao

,

Quan-Xi Qiao

THE SOLUTION OF LOCAL FRACTIONAL DIFFUSION EQUATION INVOLVING HILFER FRACTIONAL DERIVATIVE

ABSTRACT
In this present work the Yang-Fourier transform method incorporating the Laplace transform method is used to solve fractional diffusion equations involving the Hilfer fractional derivative and local fractional operator. The exact solution is obtained.
KEYWORDS
diffusion equations, Yang-Fourier transform, laplace transform, Hilfer fractional derivative, local fractional operator
PAPER SUBMITTED: 2018-04-21
PAPER REVISED: 2018-07-19
PAPER ACCEPTED: 2018-10-11
PUBLISHED ONLINE: 2019-04-14
DOI REFERENCE: https://doi.org/10.2298/TSCI180421114Q
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 3, PAGES [S809 - S814]
REFERENCES
  1. Mainardi, Francesco, Y. Luchko, and G. Pagnini. The fundamental solution of the space-time fractional diffusion equation, Fractional Calculus and Applied Analysis, 2(2007), 4, pp.153--192
  2. Langlands, T. A. M., and B. I. Henry, The accuracy and stability of an implicit solution method for the fractional diffusion equation, Journal of Computational Physics, 2(2005), 205, pp. 719-736
  3. Tadjerana, Charles, A second-order accurate numerical approximation for the fractional diffusion equation, Journal of Computational Physics, 1(2006), 213, pp. 205-213
  4. X.-J. Yang, F. Gao, Y. Ju., General Fractional Derivatives with Applications in Viscoelasticity, New York: Academic Press, 2019
  5. Yang, X.-J. General Fractional Derivatives: Theory, Methods and Applications, New York: CRC Press, 2019
  6. Saadatmandi, Abbas, and M. Dehghan, A tau approach for solution of the space fractional diffusion equation, Computers and Mathematics with Applications , 3(2011), 62, pp. 1135-1142
  7. Tomovski, et al. Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions, Integral Transforms & Special Functions, 11(2010), 21, pp. 797-814
  8. Katugampola, Udita N, A New Approach to Generalized Fractional Derivatives, Mathematics , 4(2011), 6, pp. 1--15
  9. Sandev, Trifce, R. Metzler, and Živorad Tomovski, Fractional diffusion equation with a generalized Riemann-Liouville time fractional derivative, Journal of Physics A Mathematical & Theoretical , 25(2011), 44, pp. 255203
  10. Zivorad Tomovski, Generalized Cauchy type problems for nonlinear fractional differential equations with composite fractional derivative operator, Nonlinear Analysis Theory Methods and Applications, 7(2012), 75, pp.3364-3384
  11. Qassim, M. D, K. M. Furati, and N. E. Tatar, On a Differential Equation Involving Hilfer-Hadamard Fractional Derivative, Abstract and Applied Analysis , 1085-3375(2014) , pp. 1-9
  12. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications. New York: Academic Press, 2015
  13. Saxena, Ram K., Z. Tomovski, and T. Sandev, Fractional Helmholtz and fractional wave equations with Riesz-Feller and generalized Riemann-Liouville fractional derivatives, Eprint Arxiv , 3(2014), 7, pp.24-32
  14. Yang, Xiao Jun, D. Baleanu, and H. M. Srivastava, Local fractional similarity solution for the diffusion equation defined on Cantor sets, Applied Mathematics Letters, 47(2015), 1, pp. 54-60
  15. Yang, X. J. Advanced Local Fractional Calculus and Its Applications. New York: World Science Publisher, 2012
  16. Oldham, Keith B, and J. Spanier, The fractional calculus, Mathematical Gazette , 247(1974), 56, pp.396-400
  17. Yang, X. J. Local Fractional Functional Analysis & Its Applications. Hong Kong: Asian Academic Publisher, 2011
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The solution of local fractional diffusion equation involving Hilfer fractional derivative

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