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A local derivative with new parameter was used to model diffusion. The modified equation was solved iteratively. Stability of the used method together with the uniqueness of the special solution was studied. An algorithm was proposed to derive the special solution.
PAPER REVISED: 2015-02-02
PAPER ACCEPTED: 2015-03-04
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THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S231 - S238]
  1. Kilbas, A., et al., Theory and Applications of Fractional Differential Equations, Elsevier, 2006
  2. Li, B., Q., Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer, Springer-Verlag, London, 2006
  3. Versteeg, H., Malalasekera, W., An Introduction to Computational Fluid Dynamics, Prentice Hall, Upper Saddle River, N. J. USA, 2007, pp. 262-263
  4. Smoluchowski, M. v., About Brownian Motion under the Action of External Forces and the Relationship with the Generalized Diffusion Equation (in German), Ann. Phys. 353 (1915), pp. 1103-1112
  5. Yang, X. J. et al., Cantor-Type Cylindrical-Coordinate Method for Differential Equations with Local Fractional Derivatives, Physics Letters A, 377 (2013), 28-30, pp. 1696-1700
  6. Florian C., The History of Notations of the Calculus, Annals of Mathematics, 25 (1923), 1, pp. 1-46
  7. Leonid, P., Cloud, M. J., Approximating Perfection: a Mathematician's Journey into the World of Mechanics, Princeton University Press, Princeton, N. J., USA, 2004
  8. Apostol, T. M., One-Variable Calculus with an Introduction to Linear Algebra, Wiley, New York, USA, 1967
  9. Atangana, A., Aydin, S., A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions, Abstract and Applied Analysis, 2013 (2013), ID 279681
  10. Caputo, M., Linear Models of Dissipation Whose Q is Almost Frequency Independent, Part II, Geophysical Journal International, 13 (1967), 5, pp. 529-539
  11. Atangana, A., Botha, J. F., Generalized Groundwater Flow Equation Using the Concept of Variable Order Derivative, Boundary Value Problems, 2013 (2013), pp. 53
  12. Magin, R. L., Fractional Calculus in Bioengineering, Begell House, Redding, Conn., USA, 2006
  13. Chechkin, A. V. et al., Fractional Diffusion in Inhomogeneous Media, Journal of Physics A, 38 (2005), 42, pp. L679-L684
  14. Granville, S., The Numerical Solution of Ordinary and Partial Differential Equations, Academic Press Professional, Inc., San Diego, Cal., USA, 1988
  15. Yang, X. J., Local Fractional Integral Transforms, Progress in Non-linear Science, 4 (2011), pp. 1-225
  16. Merdan, M., Mohyud-Din, S. T., A New Method for Time-Fractional Coupled-KDV Equations with Modified Riemann-Liouville Derivative, Studies in Non-linear Science, 2 (2011), 2, pp. 77-86
  17. Tan, Y., Abbasbandy S., Homotopy Analysis Method for Quadratic Riccati Differential Equation, Communications in Non-linear Science and Numerical Simulation, 13 (2008), 3, pp. 539-546
  18. Atangana, A., Drawdown in Prolate Spheroidal-Spherical Coordinates Obtained via Green's Function and Perturbation Methods, Communications in Non-linear Science and Numerical Simulation, 19 (2014), 5, pp. 1259-1269
  19. Atangana, A., A Note on the Triple Laplace Transform and its Applications to some Kind of Third- Order Differential Equation, Abstract and Applied Analysis, 2013 (2013), ID 769102
  20. Duffy, D. G., Transform Methods for Solving Partial Differential Equations, CRC Press, New York, USA, 2004
  21. Brychkov, Y. A., Multidimensional Integral Transformations, Gordon and Breach Science Publishers, Philadelphia, Penn., USA, 1992
  22. Kilicman, A., Gadain, H. E., On the Applications of Laplace and Sumudu Transforms, Journal of the Franklin Institute, 347 (2010), 5, pp. 848-862
  23. Yang, X. J., Baleanu, D., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method, Thermal Science, 17 (2013), 2, pp. 625-628
  24. Chen, Y. Q., Moore, K. L., Discretization Schemes for Fractional-Order Differentiators and Integrators, IEEE Transactions on Circuits and Systems I, 49 (2002), 3, pp. 363-367

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