THERMAL SCIENCE

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Haldun Alpaslan Peker

,

Fatma Aybike Cuha

APPLICATION OF KASHURI FUNDO TRANSFORM AND HOMOTOPY PERTURBATION METHODS TO FRACTIONAL HEAT TRANSFER AND POROUS MEDIA EQUATIONS

ABSTRACT
Integral transformations have been used for a long time in the solution of differential equations either solely or combined with other methods. These transforms provide a great advantage in reaching solutions in an easy way by transforming many seemingly complex problems into a more understandable format. In this study, we used an integral transform, namely Kashuri Fundo transform, by blending with the homotopy perturbation method for the solution of non-linear fractional porous media equation and time-fractional heat transfer equation with cubic non-linearity.
KEYWORDS
Kashuri Fundo transform, homotopy perturbation method, caputo fractional derivative, fractional heat transfer, porous media equation
PAPER SUBMITTED: 2021-10-29
PAPER REVISED: 2022-03-07
PAPER ACCEPTED: 2022-05-15
PUBLISHED ONLINE: 2022-07-23
DOI REFERENCE: https://doi.org/10.2298/TSCI2204877P
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 4, PAGES [2877 - 2884]
REFERENCES
  1. Lokenath, D., Bhatta, D., Integral Transform and Their Applications, CRC Press, Boca Raton, Fla., USA, 2014
  2. Diethelm, K., The Analysis of Fractional Differential Equations, Springer-Verlag, Berlin, Germany, 2010
  3. He, J. H., Homotopy Perturbation Method: A New Non-Linear Analytical Technique, Applied Mathematics and Computation, 135 (2003), 1, pp. 73-79
  4. Roozi, A., et al., Homotopy Perturbation Method for Special Non-linear Partial Differential Equations, Journal of King Saud University (Science), 23 (2011), 1, pp. 99-103
  5. Roul, P., Meyer, P., Numerical Solutions of Systems of Non-linear Integro-Differential Equations by Homotopy Perturbation Method, Applied Mathematical Modellling, 35 (2011), 9, pp. 4234-4242
  6. Yan, L.,M., Modified Homotopy Perturbation Method Coupled with Laplace Transform for Fractional Heat Transfer and Porous Media Equations, Thermal Science, 17 (2013), 5, pp. 1409-1414
  7. Alkan, S., A New Solution Method for Non-Linear Fractional Integro-Differential Equations, Discrete and Continuous Dynamical Systems Series S, 8 (2015), 6, pp. 1065-1077
  8. Alkan, S., Secer, A., Application of Sinc-Galerkin Method for Solving Space-Fractional Boundary Value Problems, Mathematical Problems in Engineering, 2015 (2015), ID217348
  9. Alkan, S., Secer, A., Solution of Non-Linear Fractional Boundary Value Problems with Non-Homogeneous Boundary Conditions, Applied and Computational Mathematics, 14 (2015), 3, pp. 284-295
  10. He, J. H., Variational Iteration Method- a Kind of Non-Linear Analytical Technique: Some Examples, International Journal of Non-linear Mechanics, 34 (1999), 4, pp. 609-708
  11. He, J. H., Wu, X. H., Variational Iteration Method: New Development and Applications, Computers & Mathematics with Applications, 54 (2007), 7-8, pp. 881-894
  12. Guo, S. M., et al., Fractional Variational Homotopy Perturbation Iteration Method and Its Application to a Fractional Diffusion Equation, Applied Mathematics and Computation, 219 (2013), 11, pp. 5909-5917
  13. Tatari, M., et al., Application of the Adomian Decomposition Method for the Fokker-Planck Equation, Mathematical and Computer Modelling, 45 (2007), 5-6, pp. 639-650
  14. Jafari, H., et al., Application of the Laplace Decomposition Method for Solving Linear and Non-Linear Fractional Diffusion-Wave Equations, Applied Mathematics Letters, 24 (2011), 11, pp. 1799-1805
  15. Liu, Y., Q., Approximate Solutions of Fractional Non-Linear Equations Using Homotopy Perturbation Transformation Method, Abstract and Applied Analysis, 2012 (2012), ID752869
  16. Kashuri, A., et al., Mixture of a New Integral Transform and Homotopy Perturbation Method for Solving Non-Linear Partial Differential Equations, Advances in Pure Mathematics, 3 (2013), 3, pp. 317-323
  17. Singh, B., K., Homotopy Perturbation New Integral Transform Method for Numeric Study of Space and Time- Fractional (n+1)-Dimensional Heat and Wave-Like Equations, Waves, Wavelets and Fractals, 4 (2018), 1, pp. 19-36
  18. Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
  19. Mathai, A. M., Haubold, H. J., An Introduction to Fractional Calculus, Nova Science Publishers, New York, USA, 2017
  20. Shah, K., et al., Combination of Integral and Projected Differential Transform Methods for Time-Fractional Gas Dynamics Equations, Ain Shams Engineering Journal, 9 (2018), 4, pp. 1683-1688
  21. Kashuri, A., Fundo, A., A New Integral Transform, Advances in Theoretical and Applied Mathematics, 8 (2013), 1, pp. 27-43
  22. Sumiati, I., et al., Adomian Decomposition Method and The New Integral Transform, Proceedings, 2nd African International Conference on Industrial Engineering and Operations Management, Harare, Zimbabwe, 2020, pp. 1882-1887
  23. Yan, L. M., Modified Homotopy Perturbation Method Coupled with Laplace Transform for Fractional Heat Transfer and Porous Media Equations, Thermal Science, 17 (2013), 5, pp. 1409-1414
  24. Pamuk, S., Solution of the Porous Media Equation by Adomian's Decomposition Method, Physics Letters A, 344 (2005), 2-4, pp. 184-188
  25. Ganji, D., D., Sadighi, A., Application of Homotopy Perturbation and Variational Iteration Methods to Non-Linear Heat Transfer and Porous Media Equations, Journal of Computational and Applied Mathematics, 207 (2007), 1, pp. 24-34
  26. Liu, J., Linear Stability Analysis and Homoclinic Orbit for a Generalized Non-Linear Heat Transfer, Thermal Science, 16 (2012), 5, pp. 1556-1559
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Application of Kashuri Fundo transform and homotopy perturbation methods to fractional heat transfer and porous media equations

© 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