THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Jun-Feng Lu

,

Meng-Jie Chen

VARIATIONAL APPROACH TO TIME-SPACE FRACTIONAL COUPLED BOITI-LEON-PEMPINELLI EQUATION

ABSTRACT
This paper focuses on the variational approach to a time-space fractional coupled Boiti-Leon-Pempinelli equation. The fractional system can be transformed into the original coupled Boiti-Leon-Pempinelli equation by using the fractional complex transformation. The variational approach provides three new types of soliton solutions.
KEYWORDS
variational approach, fractional complex transformation, soliton
PAPER SUBMITTED: 2023-11-01
PAPER REVISED: 2024-05-09
PAPER ACCEPTED: 2024-05-10
PUBLISHED ONLINE: 2025-07-06
DOI REFERENCE: https://doi.org/10.2298/TSCI2503757L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 3, PAGES [1757 - 1765]
REFERENCES
  1. Oldham, K. B., Spanier, J., The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press, New York, USA, 1974
  2. Samko, S. G., et al, Fractional Integrals and Derivatives Theory and Applications, Gordon and Breach, New York, USA, 1993
  3. Podlubny, I., Fractional Differential Equation, Academic Press, New York, USA, 1999
  4. He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), June, pp. 3698-3718
  5. Odibat, Z., Approximations of Fractional Integral and Caputo Fractional Derivatives, Applied Mathematics and Computing, 178 (2006), 2, pp. 527-533
  6. Yang, X. J., et al., A New Computational Approach for Solving Non-Linear Local Fractional PDEs, Journal of Computational Applied Mathematics, 339 (2018), Sept., pp. 285-296
  7. El-Ajou, A., A Modification to the Conformable Fractional Calculus with Some Applications, Alexandria Engineering Journal, 59 (2020), 4, pp. 2239-2249
  8. Oldham, K. B., Fractional Differential Equations in Electrochemistry, Advances in Engineering Soft-ware, 41 (2010), 1, pp. 9-12
  9. El-Nabulsi, R. A., On a New Fractional Uncertainty Relation and its Implications in Quantum Mechanics and Molecular Physics, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 476 (2020), 20190729
  10. He, C. H., A Variational Principle for a Fractal Nano/Microelectromechanical (N/MEMS) System, International Journal of Numerical Methods for Heat & Fluid Flow, 33 (2023), 1, pp. 351-359
  11. Lu, J., Ma, L., Numerical Analysis of Space-Time Fractional Benjamin-Bona-Mahony Equation, Thermal Science, 27 (2023), 3A, pp. 1755-1762
  12. Chen, B., Lu, J., Two Analytical Methods for Time Fractional Caudrey-Dodd-Gibbon-Sawada-Kotera Equation, Thermal Science, 26 (2022), 3B, pp. 2531-2539
  13. Zheng, S., et al., Numerical Analysis of a Fractional Micro/Nano Beam-Based Micro-Electromechanical System, Fractals, 33 (2025), 1, 2550028
  14. Li, Z. B., He, J.-H., Fractional Complex Transform for Fractional Differential Equations. Mathematical and Computational Applications, 15 (2010), 5, pp. 970-973
  15. He, J.-H., Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
  16. Ain, Q. T., He, J.-H., On Two-Scale Dimension and its Applications, Thermal Science, 23 (2019), 3B, pp. 1707-1712
  17. He, J.-H., Seeing with a Single Scale is Always Unbelieving: From Magic to Two-scale Fractal, Thermal Science, 25 (2021), 2B, pp. 1217-1219
  18. Fang, J. P., et al., Localized Structures on Periodic Background Wave of (2+1)-dimensional Boiti-Leon-Pempinelli System via an Object Reduction, Communications in Theoretical Physics, 48 (2007), 5, pp. 811-814
  19. Dai, C., Wang, Y., Periodic Structures Based on Variable Separation Solution of the (2+1)-Dimensional Boiti-Leon-Pempinelli Equation, Chaos, Solitons & Fractals, 39 (2009), 1, pp. 350-355
  20. Feng, W. G., et al., Explicit Exact Solutions for (2+1)-Dimensional Boiti-Leon-Pempinelli Equation, Communications in Non-Linear Science and Numerical Simulation, 14 (2009), 5, pp. 2013-2017
  21. Fei, J. X., et al., Symmetry Reduction and Explicit Solutions of the (2+1)-Dimensional Boiti-Leon- Pempinelli System, Applied Mathematics and Computing, 268 (2015), Oct., pp. 432-438
  22. Kumar, M., et al., Some More Similarity Solutions of the (2+1)-Dimensional BLP System, Computers & Mathematics with Applications, 70 (2015), 3, pp. 212-221
  23. Kumar, M., et al., Elliptic and Solitary Wave Solutions for Bogoyavlenskii Equations System, Couple Boiti-Leon-Pempinelli Equations System and Time-Fractional Cahn-Allen Equation, Results in Physics, 7 (2017), July, pp. 2325-2333
  24. Ma, Z. Y., et al., New Fractal Localized Structures in Boiti-Leon-Pempinelli System, Communications in Theoretical Physics, 42 (2004), 4, pp. 521-523
  25. He, J.-H., Variational Approach for Non-Linear Oscillators, Chaos, Solitons & Fractals, 34 (2007), 5, pp. 1430-1439
  26. Wang, K. L., Novel Travelling Wave Solutions for the Fractal Zakharov-Kuznetsov-Benjamin-Bona- Mahony Model, Fractals, 30 (2022), 9, 2250170
  27. Lu, J., et al., Variational Approach for Time-Space Fractal Bogoyavlenskii Equation, Alexandria Engineering Journal, 97 (2024), June, pp. 294-301
  28. Lu, J., Ma, L., Analysis of a Fractal Modification of Attachment Oscillator, Thermal Science, 28 (2024), 3A, pp. 2153-2163
  29. Lu J., Sun, Y., Analysis of the Fractional Oscillator for a Mass Attached to a Stretched Elastic Wire, Journal of Low Frequency Noise, Vibration and Active Control, 42 (2023), 4, pp. 1733-1742
  30. He, C. H., et al., Editorial: Analytical Methods for non-linear Oscillators and Solitary Waves, Frontiers in Physics, 11 (2023), 1309182
  31. He, J.-H., et al., Forced Non-linear Oscillator in a Fractal Space, Facta Universitatis Series: Mechanical Engineering, 20 (2022), 1, pp. 1-20
  32. He, J.-H., Ain, Q. T., New Promises and Future Challenges of Fractal Calculus: From Two-scale Thermodynamics to Fractal Variational Principle, Thermal Science, 24 (2020), 2A, pp. 659-681
  33. He, J.-H., et al., A Good Initial Guess for Approximating Non-Linear Oscillators by the Homotopy Per-turbation Method, Facta Universitatis Series: Mechanical Engineering, 21 (2023), 1, pp. 21-29
  34. He, J.-H., A Modified Li-He's Variational Principle for Plasma, International Journal of Numerical Methods for Heat & Fluid Flow, 31 (2021), 5, pp. 1369-1372
  35. He, J.-H., Variational Principles for Some Non-Linear Partial Differential Equations with Variable Coefficients, Chaos, Solitons & Fractals, 19 (2004), 4, pp. 847-851
  36. Lu, J., Application of Variational Principle and Fractal Complex Transformation to (3+1)-Dimensional Fractal Potential-YTSF Equation, Fractals, 32 (2024), 1, 2450027
  37. Lu, J., Variational Approach for (3+1)-Dimensional Shallow Water Wave Equation, Results in Physics, 56 (2024), 107290
  38. He, J.-H., et al., Solitary Waves Travelling along an Unsmooth Boundary, Results in Physics, 24 (2021), May, 104104
  39. He, C. H., Liu, C., Variational Principle for Singular Waves, Chaos, Solitons & Fractals, 172 (2023), July, 113566
PDF VERSION [DOWNLOAD]
Variational approach to time-space fractional coupled Boiti-Leon-Pempinelli equation

2025 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