THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Shuxian Deng

,

Ermin Wang

,

Xinxin Ge

ANALYTIC ALGORITHM FOR LOCAL FRACTIONAL CAUDREY-DODD-GIBBON-KAEADA EQUATION BASED ON THE NEW ITERATIVE METHOD

ABSTRACT
In this paper, the initial value problem is discussed for the local fractional Caudrey-Dodd-Gibbon-Kaeada equation. The fractional complex transform and the new iterative method are used to solve the problem, and the approximate analytical solutions are obtained.
KEYWORDS
Caudrey-Dodd-Gibbon-Kaeada equation, local fractional derivative, complex transform method, new iterative method
PAPER SUBMITTED: 2020-11-05
PAPER REVISED: 2021-10-01
PAPER ACCEPTED: 2021-10-01
PUBLISHED ONLINE: 2022-07-16
DOI REFERENCE: https://doi.org/10.2298/TSCI2203771D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 3, PAGES [2771 - 2778]
REFERENCES
  1. Yang, X.-J., et al., A New Family of the Local Fractional PDEs, Fundamenta Informaticae, 151 (2017), 1-4, pp. 63-75
  2. Yang, X.-J., et al., New Rheological Models Within Local Fractional Derivative, Romanian Reports in Physics, 69 (2017), 3, 113
  3. Yang, X. J., Baleanu, D., Fractal Heat Conduction Problem Solved by Local Fractional Variation Itera-tion Method, Thermal Science, 2 (2013), 17, pp. 625-628
  4. Yang, A. M., et al., Picard Successive Approximation Method for Solving Differential Equations Aris-ing in Fractal Heat Transfer with Local Fractional Derivative, Abstract and Applied Analysis, 2 (2014), 2014, pp. 1-5
  5. Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics, Fractals, 29 (2021), 7, 21501826
  6. Habib, S., et al., Study of Non-linear Hirota-Satsuma Coupled KdV and Coupled mKdV System with Time Fractional Derivative, Fractals, 29 (2021), 5, 2150108
  7. Shi, Y. Q., et al., The Multi-Wave Method for Non-linear Evolution Equations, Mathematical and Com-putational Applications, 15 (2011), 5, pp. 776-783
  8. Fan, E.G., Traveling Wave Solutions for Non-linear Equations Using Symbolic Computation, Comput-ers and Mathematics with Applications, 43 (2002), 6-7, pp. 671-680
  9. Wazwaz, A. M., Analytic Study of the Fifth Order Integrable Non-linear Evolution Equations by Using the Tanh Method, Applied Mathematics and Computation, 174 (2006), 1, pp. 289-299
  10. Wazwaz, A. M., Multiple-Soliton Solutions for the Fifth Order Caudrey-Dodd-Gibbon Equation, Ap-plied Mathematics and Computation, 197 (2008), 2, pp. 719-724
  11. Yang, Y. J., The Extended Variational Iteration Method for Local Fractional Differential Equation, Thermal Science, 25 (2021), 2, pp. 1509-1516
  12. Yang, Y. J., The Local Fractional Variational Iteration Method: A Promising Technology for Fractional Calculus, Thermal Science, 24 (2020), 4, pp. 2605-2614
  13. Nadeem, M., He, J. H., He-Laplace Variational Iteration Method for Solving the Non-linear Equations Arising in Chemical Kinetics and Population Dynamics, Journal of Mathematical Chemistry, 59 (2021), 5, pp. 1234-1245
  14. He, J.‐H., et al., Homotopy Perturbation Method for the Fractal Toda Oscillator, Fractal Fract., 5 (2021), 93
  15. He, J. H., El-Dib, Y. O., Periodic Property of the Time-Fractional Kundu-Mukherjee-Naskar Equation, Results in Physics, 19 (2020), Dec., 103345
  16. Jafari, H., Jassim, H. K., Local Fractional Series Expansion Method for Solving Laplace and Schroding-er Equations on Cantor Sets within Local Fractional Operators, International Journal of Mathematics and Computer Research, 11 (2014), 2, pp. 736-744
  17. Wang, S. Q., et al., Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative, Abstract and Applied Analysis, 2014, Article ID 176395
  18. Daftardar-Gejji, V., Jafari, H., An Iterative Method for Solving Non-linear Functional Equations, Jour-nal of Mathematical Analysis and Applications, 316 (2006), 2, pp. 753-763
  19. Bhalekar, S., Daftardar-Gejji, V., New Iterative Method: Application to Partial Differential Equations, Applied Mathematics and Computation, 203 (2008), 2, pp. 778-783
  20. Daftardar-Gejji, V., and Bhalekar, S. Solving Fractional Boundary Value Problems with Dirichlet Boundary Conditions Using a New Iterative Method, Computers & Mathematics with Applications, 59 (2010), 5, pp. 1801-1809
  21. He, J. H., Li, Z. B., Converting Fractional Differential Equations Into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
  22. Li, Z. B., et al., Exact Solutions of Time Fractional Heat Conduction Equation by the Fractional Com-plex Transform, Thermal Science, 16 (2012), 2, pp. 335-338
  23. Ain, Q. T., et al., The Fractional Complex Transform: A Novel Approach to the Time-Fractional Scho-dinger Equation, Fractals, 28 (2020), 7, 2050141
  24. Anjum, N., Ain, Q. T., Application of He's Fractional Derivative and Fractional Complex Transform for Time Fractional Camassa-Holm Equation, Thermal Science, 24 (2020), 5, pp. 3023-3030
  25. He, J. H., et al., A Fractal Modification of Chen-Lee-Liu Equation and Its Fractal Variational Principle, International Journal of Modern Physics B, 35 (2021), 21, 2150214
  26. He, J. H., Seeing with a Single Scale is Always Unbelieving: From Magic to Two-Scale Fractal, Ther-mal Science, 25 (2021), 2, pp. 1217-1219
  27. He, J. H., et al., Solitary Waves Travelling Along an Unsmooth Boundary, Results in Physics, 24 (2021), May, 104104
  28. Nadeem, M., He, J. H., The Homotopy Perturbation Method for Fractional Differential Equations: Part 2, Two-Scale Transform, International Journal of Numerical Methods for Heat & Fluid Flow, 32 (2021), 2, pp. 559-567
  29. He, J. H., et al., Evans Model for Dynamic Economics Revised, AIMS Mathematics, 6 (2021), 9, pp. 9194-9206
  30. He, J. H., et al., Variational Approach to Fractal Solitary Waves, Fractals, 29 (2021), 7, 2150199
  31. Feng, G. Q., He's Frequency Formula to Fractal Undamped Duffing Equation, Journal of Low Frequen-cy Noise Vibration and Active Control, 40 (2021), 4, pp. 1671-1676
  32. Tian, Y., Liu, J., Direct Algebraic Method for Solving Fractional Fokas Equation, Thermal Science, 25 (2021), 3, pp. 2235-2244
  33. Han, C., et al., Numerical Solutions of Space Fractional Variable-Coefficient KdV-Modified KdV Equa-tion by Fourier Spectral Method，Fractals, 29 (2021), 8, pp. 1-19
  34. Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics, Fractals, 29 (2021), 7, 21501826
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Analytic algorithm for local fractional Caudrey-Dodd-Gibbon-Kaeada equation based on the new iterative method

© 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