THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Run-Qing Cui

,

Tao Ban

AN ANALYTICAL SOLUTION FOR A FRACTIONAL HEAT-LIKE EQUATION WITH VARIABLE COEFFICIENTS

ABSTRACT
The fractional power series method is used to solve a fractional heat-like equations with variable coefficients. The solution process is elucidated, and the results show that the method is simple but effective.
KEYWORDS
fractional power series, fractional heat-like equations, variable coefficients, caputo fractional derivative
PAPER SUBMITTED: 2016-08-05
PAPER REVISED: 2016-08-23
PAPER ACCEPTED: 2016-10-26
PUBLISHED ONLINE: 2017-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI160805065C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 4, PAGES [1759 - 1764]
REFERENCES
  1. Hu, Y., He, J.-H., On Fractal Space-Time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 773-777
  2. Wazwaz, A. M., Gorguis, A., Exact Solutions for Heat-Like and Wave-Like Equations with Variable Coefficients, Applied Mathematics and Computation, 149 (2004), 1, pp. 15-29
  3. Adomian, G., A Review of the Decomposition Method in Applied Mathematics, Journal of Mathemati-cal Analysis and Applications, 135 (1988), 2, pp. 501-544
  4. Sari, M., et al., A Solution to the Telegraph Equation by Using DGJ Method, International Journal of Nonlinear Science, 17 (2014), 1, pp. 57-66
  5. El-Ajou, et al., New Results on Fractional Power Series: Theories and Applications, Entropy, 15 (2013), 12, pp. 5305-5323
  6. Elsaid, A., Fractional Differential Transform Method Combined with the Adomian Polynomials, Applied Mathematics and Computation, 218 (2012), 12, pp. 6899-6911
  7. Cascaval, R. C., et al., Fractional Telegraph Equations, Journal of Mathematical Analysis and Applica-tions, 276 (2002), 1, pp. 145-159
  8. He, J.-H., Variational Iteration Method-a Kind of Non-Linear Analytical Technique: Some Examples, International Journal of Nonlinear Mechanics, 34 (1999), 4, pp. 699-708
  9. He, J.-H., Homotopy Perturbation Method: A New Nonlinear Analytical Technique, Applied Mathemat-ics and Computation, 135, (2003), 1, pp. 73-79
  10. He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
  11. Duan, J. S., et al. The Adomian Decomposition Method with Convergence Acceleration Techniques for Nonlinear Fractional Differential Equations, Computers & Mathematics with Applications, 66 (2013), 5, pp. 728-736
  12. Benghorbal, M. M., Corless, R. M., Power Series Solutions of Fractional Differential Equations. Int. J. Pure Appl. Math., 15 (2004), 3, pp. 333-352
  13. Abu-Gdairi, R., et al., An Expansion Iterative Technique for Handling Fractional Differential Equations Using Fractional Power Series Scheme. Journal of Mathematics & Statistics, 11 (2015), 2, pp. 29-38
  14. Al-Refai, M., et al., An Efficient Series Solution for Fractional Differential Equations, Abstract & Ap-plied Analysis, 2014 (2014), ID 891837
  15. Secer, A., Approximate Analytic Solution of Fractional Heat-Like and Wave-Like Equations with Vari-able Coefficients Using the Differential Transforms Method, Advances in Difference Equations, 198 (2012), Dec., pp. 1-10
  16. Atangana, A., Exact Solutions Fractional Heat-Like and Wave-Like Equations with Variable Coeffi-cients, Scientific Reports, 2 (2013), 2, pp. 1-5
  17. Atangana0 A., Kilicman A.,The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations, Abstract & Applied Analysis, 2013 (2013), ID 737481
  18. Yulita, M. R., et al., Variational Iteration Method for Fractional Heat- and Wave-Like Equations, Non-linear Analysis Real World Applications, 10 (2009), 3, pp. 1854-1869
  19. Podlubny, I., The Laplace Transform Method for Linear Differential Equations of the Fractional Order, in Fractional Differential Equations, Academic Press, San Diego, Cal., USA, 1999
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An analytical solution for a fractional heat-like equation with variable coefficients

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, 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