International Scientific Journal

Authors of this Paper

External Links


The fractal derivative is adopted to describe the non-linear fractional wave equation in a fractal space. A variational principle is successfully established by the semi-inverse method. The two-scale method and He’s exp-function are used to solve the equation, and a good result is obtained.
PAPER REVISED: 2020-06-17
PAPER ACCEPTED: 2020-06-18
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 2, PAGES [1243 - 1247]
  1. He, J. H., Generalized Equilibrium Equations for Shell Derived from a Generalized Variational Principle, Applied Mathematics Letters, 64 (2017), Feb., pp. 94-100
  2. He, J. H., An Alternative Approach to Establishment of a Variational Principle for the Torsional Problem of Piezoelastic Beams, Applied Mathematics Letters, 52 (2016), Feb., pp. 1-3
  3. He, J. H., Generalized Variational Principles for Buckling Analysis of Circular Cylinders, Acta Mechanica, 231 (2020), Dec., pp. 899-906
  4. He, J. H., The Simpler, The Better: Analytical Methods for Non-Linear Oscillators and Fractional Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp.1252-1260
  5. He, J. H., Variational Principle and Periodic Solution of the Kundu-Mukherjee-Naskar Equation, Results in Physics, 17 (2020), June, 103031
  6. Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals, 29 (2019), 8, 1950134
  7. He, J. H., A Fractal Variational Theory for 1-D Compressible Flow in a Microgravity Space, Fractals, 28 (2020), 2, 2050024
  8. Shen, Y., He, J. H., Variational Principle for a Generalized KdV-Equation in a Fractal Space, Fractals, 20 (2020), 4, 2050069
  9. He, J. H., A Short Review on Analytical Methods for to a Fully Fourth Order Non-Linear Integral Boundary Value Problem with Fractal Derivatives, International Journal of Numerical Methods for Heat and Fluid-Flow, 30 (2020), 11, pp. 4933-4934
  10. He, J. H., A Fractal Variational Theory for 1-D Compressible Flow in a Microgravity Space, Fractals, 28 (2020), 2, 2050024
  11. He, J. H., Fractal Calculus and Its Geometrical Explanation. Results in Physics, 10 (2018), Sept., pp. 272-276
  12. Li, X. J., et al., A Fractal Two-Phase Flow Model for the Fiber Motion in a Polymer Filling Process, Fractals, 28 (2020), 5, 2050093
  13. Wang, Y., et al., A Fractal Derivative Model for Snow's Thermal Insulation Property, Thermal Science, 23 (2019), 4, pp. 2351-2354
  14. Liu, H. Y., et al., A Fractal Rate Model for Adsorption Kinetics at Solid/Solution Interface, Thermal Science, 23 (2019), 4, pp. 2477-2480
  15. He, C. H., et al., Taylor Series Solution for Fractal Bratu-Type Equation Arising in Electrospinning Process, Fractals, 28, (2020), 1, 2050011
  16. Zhang, J. J., et al., Some Analytical Methods for Singular Boundary Value Problem in a Fractal Space, Appl. Comput. Math., 18 (2019), 3, pp. 225-235
  17. Wang, K. L., et al., Physical Insight of Local Fractional Calculus and Its Application Fractional Kdv-Burgers-Kuramoto Equation, Fractals, 27 (2019), 7, 1950122
  18. Wang, K. L., Wang, K. J., A Modification of the Reduced Differential Transform Method for Fractional Calculus, Thermal Science, 22 (2018), 4, pp. 1871-1875
  19. Wang, K. L, Yao, S. W., Numerical Method for Fractional Zakharov-Kuznetsov Equations with He's Fractional Derivative, Thermal Science, 23 (2019), 4, pp. 2163-2170
  20. Bekir, A., Boz, A., Exact Solutions for a Class of Non-Linear Partial Differential Equations Using Exp-Function Method, Int. J. Non-Linear Sci. Num., 8 (2007), 4, pp. 505-512
  21. 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
  22. He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133
  23. Ain, Q. T., He, J. H., On Two-Scale Dimension and Its Applications, Thermal Science, 23 (2019), 3B, pp. 1707-1712
  24. He, J. H., Thermal Science for the Real World: Reality and Challenge, Thermal Science, 24 (2020), 4, pp. 2289-2294
  25. He, J. H., Exp-Function Method for Fractional Differential Equations, International Journal of Non-Linear Sciences and Numerical Simulation, 14 (2013), 6, pp. 363-366
  26. Ji, F. Y., et al., A Fractal Boussinesq Equation for Non-Linear Transverse Vibration of a Nanofiber-Reinforced Concrete Pillar, Applied Mathematical Modelling, 82 (2020), June, pp. 437-448
  27. He, J. H., et al., Difference Equation vs. Differential Equation on Different Scales, International Journal of Numerical Methods for Heat and Fluid-Flow, On-line first,, 2020
  28. Zhang, S., et al., Simplest Exp-Function Method for Exact Solutions of Mikhauilov-Novikov-Wang Equation, Thermal Science, 23 (2019), 4, pp. 2381-2388
  29. He, J. H., Asymptotic Methods for Solitary Solutions and Compactons, Abstr. Appl. Anal., 2012 (2012), ID916793
  30. He, J. H., Wu, X. H., Exp-Function Method for Non-Linear Wave Equations, Chaos Soliton. Fract., 30 (2006), 3, pp. 700-708
  31. Wu, X. H., He, J. H., Solitary Solutions, Periodic Solutions and Compacton-Like Solutions Using the Exp-Function Method, Comput. Math. Application, 54 (2007), 7-8, pp. 966-986
  32. Wang, K. L., et. al., A Fractal Variational Principle for the Telegraph Equation with Fractal Derivatives, Fractals, 28 (2020), 4, 2050058
  33. Wang, K. L., He's Frequency Formulation for Fractal Nonlinear Oscillator Arising in a Microgravity Space, Numerical Methods for Partial Differential Equations, On-line first, 22584, 2020
  34. Wang, K. L., A Novel Approach for Fractal Burgers-BBM Equation and its Variational Principle, 2020, Fractals, On-line first,, 2020
  35. Wang, K. L., Effect of Fangzhu's Nanoscale Surface Morphology on Water Collection, Mathematical Method in the Applied Sciences, On-line first,, 2020
  36. Wang, K. J., Wang, K. L., Variational Principles for Fractal Whitham-Broer-Kaup Equations in Shallow Water, Fractals, On-line first,, 2020
  37. Wang, K. J., A New Fractional Nonlinear Singular Heat Conduction Model for the Human Head Considering the Effect of Febrifuge, Eur. Phys. J. Plus, 135 (2020), Nov., 871
  38. Wang, K. J., Variational Principle and Approximate Solution for the Generalized Burgers-Huxley Equation With Fractal Derivative, Fractals, On-line first,, 2020
  39. Wang, K. J, Variational Principle and Approximate Solution for the Fractal Vibration Equation in a Microgravity Space, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, On-line first,, 2020
  40. Wang, K. J. , On a High-Pass Filter Described by Local Fractional Derivative, Fractals, 28 (2020), 3, 2050031

© 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