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APPROXIMATE ANALYTICAL SOLUTION FOR MODIFIED KORTEWEG-DE VRIES EQUATION WITH LOCAL FRACTIONAL DERIVATIVE VIA NEW ITERATIVE METHOD

ABSTRACT
In this paper, we obtain the approximate analytical solution of variable coefficients modified Korteweg-de Vries equation with local fractional derivative by using new iterative method.
KEYWORDS
PAPER SUBMITTED: 2020-05-01
PAPER REVISED: 2020-07-15
PAPER ACCEPTED: 2020-07-20
PUBLISHED ONLINE: 2020-11-27
DOI REFERENCE: https://doi.org/10.2298/TSCI2006027D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Issue 6, PAGES [4027 - 4032]
REFERENCES
  1. Zhong, W. P., et al., Applications of Yang-Fourier Transform to Local Fractional Equations with Local Fractional Derivative and Local Fractional Integral, Advanced Materials Research, 461 (2012), 1, pp. 306-310
  2. Liu, C. S., On the Local Fractional Derivative of Everywhere Non-Differentiable Continuous Functions on Intervals, Communications in Nonlinear Science and Numerical Simulation, 42 (2017), 1, pp. 229-235
  3. Yang, X. J., et al., Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets, Applied Mathematics Letters, 47 (2015), 4, pp. 54-60
  4. Bayour, B., Torres, D., Existence of Solution to A Local Fractional Nonlinear Differential Equation, Journal of Computational and Applied Mathematics, 312 (2017), 100, pp. 127-133
  5. Yang, X. J., Local Fractional Partial Differential Equations with Fractal Boundary Problems, Advances in Computational Mathematics and its Applications, 1 (2012), 1, pp. 60-63
  6. Yang, X. J., et al., On a Fractal LC-Electric Circuit Modeled by Local Fractional Calculus, Communications in Nonlinear Science and Numerical Simulation, 47 (2017), 100, pp. 200-206
  7. Calogero, F., Degasperis, A., A Modified Korteweg-de Vries Equation, Physica D: Nonlinear Phenomena, 1 (1998), 28, pp. 237-237
  8. Buslaev, V. S., et al., Scattering Theory for the Korteweg-De Vries (KdV) Equation and Its Hamiltonian Interpretation, Physica D: Nonlinear Phenomena, 1-3 (1986), 18, pp. 255-266
  9. Pomeau, Y. A., et al., Stuctural Stability of the Korteweg-de Vries Solitons under a Singular Perturbation, Physica D: Nonlinear Phenomena, 1 (1988), 31, pp. 127-134
  10. Osborne, A. R., Segre, E., Numerical Solutions of the Korteweg-de Vries Equation using the Periodic Scattering Transform μ-Representation, Physica D: Nonlinear Phenomena, 3 (1990), 44, pp. 575-604
  11. Grimshaw, R., et al., Solitary Waves with Damped Oscillatory Tails: an Analysis of the Fifth-Order Korteweg-de Vries Equation, Physica D-nonlinear Phenomena, 4 (1994), 77, pp. 473-485
  12. Lv, Y. G., et al., Study on the Effect of Micro Geometric Structure on Heat Conduction in Porous Media Subjected to Pulse Laser, Chemical Engineering Science, 17 (2006), 61, pp. 5717-5725
  13. Tseng, C. Y., Tsao, H. K., Rate of Diffusion-Limited Reactions for a Fractal Aggregate of Reactive Spheres, Journal of Chemical Physics, 7 (2002), 117, pp. 3448-3453
  14. Huai, X. L., et al., Analysis of the Effective Thermal Conductivity of Fractal Porous Media, Applied Thermal Engineering, 17-18 (2007), 27, pp. 2815-2821
  15. Xu, P., et al., Heat Conduction in Fractal Tree-Like Branched Networks, International Journal of Heat and Mass Transfer, 19-20 (2006), 49, pp. 3746-3751
  16. He, J. H., Liu, F. J., Local Fractional Variational Iteration Method for Fractal Heat Transfer in Silk Cocoon Hierarchy, Nonlinear Science Letters A, 1 (2013), 4, pp. 15-20
  17. Liu, C. F., et al., Reconstructive Schemes for Variational Iteration Method within Yang-Laplace Transform with Application to Fractal Heat Conduction Problem, Thermal Science, 17 (2013), 3, pp. 715-721
  18. Jafari, H., Kamil, H. J., Local Fractional Variational Iteration Method for Solving Nonlinear Partial Differential Equations within Local Fractional Operators, Applications and Applied Mathematics, 2 (2015), 10, pp. 1055-1065
  19. Jafari, H., Kamil, H. J., Application of the Local fractional Adomian Decomposition and Series Expansion Methods for Solving Telegraph Equation on Cantor Sets Involving Local Fractional Derivative Operators, Journal of Zankoy Sulaimani-Part A, 2 (2015), 17, pp. 15-22
  20. Daftardar, G. V., Jafari, H., An Iterative Method for Solving Nonlinear Functional Equations, Journal of Mathematical Analysis and Applications, 316 (2006), 2, pp. 753-763
  21. Bhalekar, S., Daftardar, G. V., New Iterative Method: Application to Partial Differential Equations, Applied Mathematics and Computation, 203 (2008), 2, pp. 778-783
  22. Daftardar, G. V., 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
  23. Yang, X. J., Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher Limited, Hong Kong, 2011

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