THERMAL SCIENCE

International Scientific Journal

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Ji-Huan He

,

Zheng-Biao Li

CONVERTING FRACTIONAL DIFFERENTIAL EQUATIONS INTO PARTIAL DIFFERENTIAL EQUATIONS

ABSTRACT
A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.
KEYWORDS
modified Riemann Liouville derivative, time fractional heat conduction equation, fractional kdv equation
PAPER SUBMITTED: 2011-05-03
PAPER REVISED: 2011-05-20
PAPER ACCEPTED: 2011-07-11
DOI REFERENCE: https://doi.org/10.2298/TSCI110503068H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2012, VOLUME 16, ISSUE Issue 2, PAGES [331 - 334]
REFERENCES
  1. Li, Z.B., He, J.H., Fractional Complex Transform for Fractional Differential Equations, Mathematical and Computational Applications, 15(2010), 5, pp. 970-973
  2. Li, Z.B., An Extended Fractional Complex Transform, Journal of Nonlinear Science and Numerical Simulation, 11(2010), s, pp. 0335-0337
  3. Jumarie, G., Cauchy's integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order, Applied Mathematics Letters, 23(2010), 12, pp. 1444-1450
  4. Jumarie, G., Fractional partial differental equations and modified Riemann- Liouville derivative new methods for solution, Journal of Applied Mathematics and Computing, 24(2007), 1-2, pp. 31-48
  5. Jumarie, G., modified Riemann-Liouville Derivative and Fractional Taylor series of Non-differentiable Functions Further Results, Computers and Mathematics with Applications, 51 (2006), 9-10, pp. 1367-1376
  6. He J.H., Analytical methods for thermal science-An elementary introduction, Thermal Science, 15(2011), s, pp. S1-S3
  7. He, J.H., A New Fractal Derivation, Thermal Science, 15(2011), s, pp. S145-S147
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Converting fractional differential equations into partial differential equations

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