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Xiuquan Zhang

APPROXIMATE ANALYTICAL SOLUTION TO THE KUDRYASHOV-SINELSHCHIKOV EQUATION WITH HE'S FRACTIONAL DERIVATIVE

ABSTRACT
In this paper, the Adomian decomposition method was employed successfully to solve the Kudryashov-Sinelshchikov equation involving He's fractional derivatives, and an approximate analytical solution was obtained.
KEYWORDS
Kudryashov-Sinelshchikov equation, He’s fractional derivative, Adomian decomposition method
PAPER SUBMITTED: 2021-08-05
PAPER REVISED: 2022-07-15
PAPER ACCEPTED: 2022-07-19
PUBLISHED ONLINE: 2023-06-11
DOI REFERENCE: https://doi.org/10.2298/TSCI2303795Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 3, PAGES [1795 - 1802]
REFERENCES
  1. Adomian, G., A Review of the Decomposition Method in Applied Mathematics, Journal of Mathematical Analysis and Applications, 135 (1988), 2, pp. 501-544
  2. He, J. H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
  3. Randruut, M., On the Kudryashov-Sinelshchikov Equation for Waves in Bubbly Liquids, Physics Letters A, 42 (2011), 375, pp. 3687-3692
  4. Randruut, M., Braun, M., Cnoidal Waves Governed by the Kudryashov-Sinelshchikov Equation, Physics Letters A,31-33 (2013), 377, pp. 1868-1874
  5. Coclite, G. M., Ruvo, L. D., Existence Results for the Kudryashov-Sinelshchikov Olver Equation, Proceedings of the Royal Society of Edinburgh Section A Mathematics, 2 (2020), 151, pp. 1-26
  6. Seadawy, A. R., et al., Non-linear Wave Solutions of the Kudryashov-Sinelshchikov Dynamical Equation in Mixtures Liquid-Gas Bubbles Under the Consideration of Heat Transfer and Viscosity, Journal of Taibah University for Science, 1 (2019), 13, pp. 1060-1072
  7. Nadjafikhah, M., Shirvani-Sh, V., Lie Symmetry Analysis of Kudryashov-Sinelshchikov Equation, Mathematical Problems in Engineering ,3 (2011), 1, pp. 505-515
  8. Randrueuet, M., Braun, M., On Identical Traveling-Wave Solutions of the Kudryashov Sinelshchikov and Related Equations, International Journal of Non-Linear Mechanics, 1 (2014), 5, pp. 206-211
  9. Gupta, A. K., Ray, S. S., On the Solitary Wave Solution of Fractional Kudryashov-Sinelshchikov Equation Describing Non-linear Wave Processes in a Liquid Containing Gas Bubbles, Applied Mathematics and Computation, 298 (2017), 1, pp. 1-12
  10. Ak, T., et al., Polynomial and Rational Wave Solutions of Kudryashov-Sinelshchikov Equation and Numerical Simulations for Its Dynamic Motions, Journal of Applied Analysis and Computation, 5 (2020), 10, pp. 2145-2162
  11. Guner, O., et al., Dark Soliton and Periodic Wave Solutions of Non-linear Evolution Equations, Advances in Difference Equations, 1 (2013), 2013, pp. 1-11
  12. Qian, M. Y., He, J. H., Collection of Polymer Bubble as a Nanoscale Membrane, Surfaces and Interfaces, 28 (2022), Dec., 101665
  13. He, J. H., et al., The Maximal Wrinkle Angle During the Bubble Collapse and Its Application to the Bubble Electrospinning, Frontiers in Materials, 8 (2022), Feb., 800567
  14. Lin, L., et al., Fabrication of PVDF/PES Nanofibers with Unsmooth Fractal Surfaces by Electrospinning: A General Strategy and Formation Mechanism, Thermal Science, 25 (2021), 2, pp. 1287-1294
  15. 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
  16. Wang, K. L., Yao, S. W., He's Fractional Derivative for the Evolution Equation, Thermal Science, 24 (2020), 4, pp. 2507-2513
  17. Lu, D. C., et al., Numerical Solutions of Coupled Non-linear Fractional KdV Equations Using He's Fractional Calculus, International Journal of Modern Physics B, 35 (2021), 3, 2150023
  18. Tian, D., et al. Fractal N/MEMS: From Pull-in Instability to Pull-in Stability, Fractals, 29 (2021), 2, 2150030
  19. He, C. H., et al., A Fractal Model for the Internal Temperature Response of a Porous Concrete, Applied and Computational Mathematics, 21 (2022), 1, pp. 71-77
  20. He, C. H., A Variational Principle for a Fractal Nano/Microelectromechanical (N/MEMS) System, International Journal of Numerical Methods for Heat & Fluid Flow, 33 (2022) 1, pp. 351-359
  21. He, C. H., et al., A Modified Frequency-Amplitude Formulation for Fractal Vibration Systems, Fractals, 30 (2022), 3, 2250046
  22. Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics, Fractals, 29 (2021), 7, 2150182
  23. He, J. H., et al., Evans Model for Dynamic Economics Revised, AIMS Mathematics, 6( 2021), 9, pp. 9194-9206
  24. He, J. H., El-Dib, Y. O., Homotopy Perturbation Method with Three Expansions for Helmholtz-Fangzhu Oscillator, International Journal of Modern Physics B, 35 (2021), 24, 2150244
  25. He, C. H., El-Dib, Y.O.,A Heuristic Review on the Homotopy Perturbation Method for Non-Conservative Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 41(2022), 2, pp. 572-603
  26. Mahmoudi, Y., A New Modified Adomian Decomposition Method for Solving a Class of Hypersingular Integral Equations of Second Kind, Journal of Computational and Applied Mathematics, 255 (2014), 1, pp. 737-742
  27. Wazwaz, A. M., Adomian Decomposition Method for a Reliable Treatment of the Emden-Fowler Equation, Applied Mathematics and Computation, 2 (2005), 161, pp. 543-560
  28. Elsaid, A., Fractional Differential Transform Method Combined with the Adomian Polynomials, Applied Mathematics and Computation, 218 (2012), 12, pp. 6899-6911
  29. Wang, P., et al., Study on Vibration Response of a Non-Unform Beam with Non-linear Boundary Condition, Facta Universitatis Series: Mechanical Engineering, 19 (2021), 4, pp. 781-804
  30. 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
  31. Mishra, H. K., Tripathi, R., Homotopy Perturbation Method of Delay Differential Equation Using He's Polynomial with Laplace Transform, Proceedings of the National Academy of Sciences India Section A, 90 (2020), 2, pp. 289-298
  32. Ain, Q. T., He, J. H., On Two-scale Dimension and its Applications, Thermal Science, 23 (2019), 3B, pp. 1707-1712
  33. He, J. H., Seeing with a Single Scale is Always Unbelieving: From Magic to Two-Scale Fractal, Thermal Science, 25 (2021), 2, pp. 1217-1219
  34. Ain, Q. T., et al., The Fractional Complex Transform: A Novel Approach to the Time-Fractional Schrodinger Equation, Fractals, 28 (2020), 7, 2050141
  35. He, J. H., El-Dib, Y. O., A Tutorial Introduction to the Two-scale Fractal Calculus and its Application to the Fractal Zhiber-Shabat Oscillator, Fractals, 29 (2021), 8, 2150268
  36. He, J. H., Qian, M. Y., A Fractal Approach to the Diffusion Process of Red Ink in a Saline Water, Thermal Science, 26 (2022), 3B, pp. 2447-2451
  37. Qian, M. Y., He, J. H., Two-Scale Thermal Science for Modern Life - Making the Impossible Possible, Thermal Science, 26 (2022), 3B, pp. 2409-2412
  38. Yau, H. T., Generalized Projective Chaos Synchronization of Gyroscope Systems Subjected to Dead-Zone Non-linear Inputs, Physics Letters A, 372 (2008), 14, pp. 2380-2385
  39. Lin, J. S., et al., Synchronization of Unidirectional Coupled Chaotic Systems with Unknown Channel Time-Delay: Adaptive Robust Observer-Based Approach, Chaos, Solitons and Fractals, 26 (2005), 3, pp. 971-978
  40. Chen, C. L., et al., Terminal Sliding Mode Control for Aeroelastic Systems, Nonlinear Dynamics, 70 (2012), 3, pp. 2015-2026
  41. Yau, H. T., Yan, J. J., Adaptive Sliding Mode Control of a High-Precision Ball-Screw-Driven Stage, Nonlinear Analysis B, 10 (2009), 3, pp. 1480-1489
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Approximate analytical solution to the Kudryashov-Sinelshchikov equation with he's fractional derivative

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