THERMAL SCIENCE

International Scientific Journal

A DECOMPOSITION METHOD FOR SOLVING DIFFUSION EQUATIONS VIA LOCAL FRACTIONAL TIME DERIVATIVE

ABSTRACT
In this paper a decomposition method based on Daftardar-Jafari method is applied for solving diffusion equations involving local fractional time derivatives. The convergence of this method for solving these type of equations is proved.
KEYWORDS
PAPER SUBMITTED: 2014-10-10
PAPER REVISED: 2015-01-20
PAPER ACCEPTED: 2015-02-12
PUBLISHED ONLINE: 2015-08-02
DOI REFERENCE: https://doi.org/10.2298/TSCI15S1S23J
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S123 - S129]
REFERENCES
  1. Baleanu, D., et al., Fractional Calculus Models and Numerical Methods, (Series on Complexity, Nonlinearity and Chaos), World Scientific, Singapore, 2012
  2. Jafari, H., An Introduction to Fractional Differential Equations (in Persian), Mazandaran University Press, Babolsar, Iran, 2013
  3. Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, Cal., USA, 1999
  4. Atangana, A., Bildik, N., The Use of Fractional Order Derivative to Predict the Groundwater Flow, Mathematical Problems in Engineering, 2013 (2013), ID 543026
  5. 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
  6. Nigmatullin, R. R., The Realization of the Generalized Transfer Equation in a Medium with Fractal Geometry, Phys Status Solidi B, 133 (1986), 1, pp. 425-430
  7. Jafari, H., Daftardar-Gejji, V., Solving Linear and Non-linear Fractional Diffusion and Wave Equations by Adomian Decomposition, Applied Mathematics and Computation, 180 (2006), 2, pp. 488-497
  8. Chuna, C., et al., Numerical Method for the Wave and Non-linear Diffusion Equations with the Homotopy Perturbation Method, Computers and Mathematics with Applications, 57 (2009), 7, pp. 1226-1231
  9. Saha Ray, S., Bera, R. K., An Approximate Solution of a Non-linear Fractional Differential Equation by Adomian Decomposition Method, Applied Mathematics and Computation, 167 (2005), 1, pp. 561-571
  10. Saha Ray, S., Bera, R. K., Analytical Solution of a Fractional Diffusion Equation by Adomian Decomposition Method, Applied Mathematics and Computation, 174 (2006), 1, pp. 329-336
  11. Cao, Y., et al., Local Fractional Functional Method for Solving Diffusion Equations on Cantor Sets, Abstract and Applied Analysis, 2014 (2014), doi:10.1155/2014/803693
  12. Wang, S., et al., Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative, Abstract and Applied Analysis, 2014 (2014), doi:10.1155 /2014/176395
  13. Yang, Y., et al, A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators, Abstract and Applied Analysis 2013 (2013), doi:10.1155/2013/202650
  14. Yang, A., et al., Analytical Solutions of the One-Dimensional Heat Equations Arising in Fractal Transient Conduction with Local Fractional Derivative, Abstract and Applied Analysis, 2013 (2013), doi:10.1155/2013/462535
  15. Yang, X. J., Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher, Hong Kong, 2011
  16. Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
  17. Yang, X. J., et al., Fractal Boundary Value Problems for Integral and Differential Equations with Local Fractional Operators, Thermal Science, (2013), DOI: 10.2298/TSCI130717103Y
  18. Daftardar-Gejji, V., Jafari, H., An Iterative Method for Solving Non-linear Functional Equations, J. Math. Anal. Appl., 316 (2006), 2, pp. 753-763
  19. Bhalekar, S., Daftardar-Gejji, V., Convergence of the New Iterative Method, International Journal of Differential Equations, 2011 (2011), ID 989065

© 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