International Scientific Journal

Authors of this Paper

External Links


In this paper, He's fractional derivative is adopted to establish fractional evolution equations in a fractal space. He's fractional complex transform is used to convent the fractional evolution equation into its traditional partner, and the homotopy perturbation method is used to solve the equations. Some illustrative examples are presented to show that the proposed technology is very excellent.
PAPER REVISED: 2019-10-28
PAPER ACCEPTED: 2019-10-28
CITATION EXPORT: view in browser or download as text file
  1. He, J. H., A Tutorial Review on Fractal Space Time and Fractional Calculus, Int. J. Theor. Phys., 53 (2014), 11, pp. 3698-718
  2. Anjum, N., He, J. H., Laplace Transform: Making The Variational Iteration Method Easier, Applied Mathematics Letters, 92 (2019), June, pp. 134-138
  3. He, J. H., Some Asymptotic Methods for Strongly Non-linear Equations, International Journal of Modern Physics B, 20 (2006), 10, pp. 1141-1199
  4. Baleanu, D., et al., A Modified Fractional Variational Iteration Method for Solving Non-linear Gas Dynamic and Coupled KdV Equations Involving Local Fractional Operator, Thermal Science , 22 (2018), Suppl. 1, pp. S165-S175
  5. Durgun, D. D., Konuralp, A., Fractional Variational Iteration Method for Time-Fractional Non-linear Functional Partial Differential Equation Having Proportional Delays, Thermal Science 22 (2018), Suppl. 1, pp. S33-S46
  6. He, J. H., Fractal Calculus and Its Geometrical Explanation, Result in physics, 10 (2018), Sept., pp. 272-276
  7. Hu, Y., He, J. H., On Fractal Space-Time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 773-777
  8. Wang, K. J., On a High-Pass Filter Described by Local Fractional Derivative, Fractals, On-line first,, 2020
  9. Wang, K. L., Yao, S. W., Numerical Method for Fractional Zakharov-Kuznetsov Equation with He's Fractional Derivative, Thermal Science, 23 (2019), 4, pp. 2163-2170
  10. He, J. H., Ji, F. Y., Taylor Series Solution for Lane-Emden Equation, Journal of Mathematical Chemistry, 57 (2019), 8, pp. 1932-1934
  11. He, J. H., The Simplest Approach to Non-linear Oscillators, Results in Physics, 15 (2019), Dec., ID 102546
  12. He, J. H., Homotopy Perturbation Technique, Computer Methods in Applied Mechanics and Engineering. 178 (1999), 3-4, pp. 257-262
  13. He, J. H., A Coupling Method of a Homotopy Technique and a Perturbation Technique for Non-linear Problems, International Journal of Non-Linear Mechanics, 35 (2000), 1, pp. 37-43
  14. He, J. H., Application of Homotopy Perturbation Method to Non-linear Wave Equation, Chaos, Solitons and Fractals, 26 (2005), 3, pp. 695-700
  15. He, J. H., Homotopy Perturbation Method with an Auxiliary Term. Abstract and Applied Analysis, 2012 (2012), ID 857612
  16. He, J. H., Homotopy Perturbation Method with Two Expanding Parameters, Indian Journal of Physics, 88 (2014), 2, pp. 193-196
  17. Adamu, M. Y., Ogenyi, P. New Approach to Parameterized Homotopy Perturbation Method, Thermal Science , 22 (2018), 4, pp. 1865-1870
  18. Ren, Z. F., et al., He's Multiple Scales Method for Non-linear Vibrations, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1708-1712
  19. Liu, Z. J., et al. Hybridization of Homotopy Perturbation Method and Laplace Transformation for the Partial Differential Equations. Thermal Science, 21 (2017), 4, pp. 1843-1846
  20. Wu, Y., He, J. H., Homotopy Perturbation Method for Non-linear Oscillators with Coordinate Dependent Mass. Results in Physics, 10 (2018), Sept., pp. 270-271
  21. He, J. H. ,A Modified Li-He's Variational Principle for Plasma, International Journal of Numerical Methods for Heat and Fluid Flow, On-line first,, 2019
  22. He, J. H., Lagrange Crisis and Generalized Variational Principle for 3D unsteady flow, International Journal of Numerical Methods for Heat and Fluid Flow, On-line first,, 2019
  23. He, J. H., Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
  24. Li, Z. B., He, J. H., Fractional Complex Transform for Fractional Differential Equations, Math. Comput. Appl., 15 (2010), 5, pp. 970-973
  25. 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
  26. He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Sci-ence, 23 (2019), 4, pp. 2131-2133
  27. Ain, Q. T., He, J. H., On Two-Scale Dimension and Its Applications, Thermal Science, 23 (2019), 3B, pp. 1707-1712
  28. Wang, Y., et al., A Variational Formulation for Anisotropic Wave Traveling in a Porous Medium, Fractals, 27 (2019), 4, ID 1950047
  29. Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, ID 1950134
  30. He, J. H., Sun, C., A Variational Principle for a Thin Film Equation, Journal of Mathematical Chemistry., 57 (2019), 9, pp. 2075-2081
  31. Wang, K. L., et al., Physical Insight of Local Fractional Calculus and its Application to Fractional KdV-Burgers-Kuramoto Equation, Fractals, 27 (2019), 8, ID 1950122
  32. Li, X. X., et al., A Fractal Modification Of The Surface Coverage Model For An Electrochemical Arsenic Sensor, Electrochimica Acta, 296 (2019), Feb., pp. 491-493
  33. Wang, Q. L., et al., Fractal Calculus and Its Application to Explanation of Biomechanism of Polar Bear Hairs, Fractals, 26 (2018), 6, 1850086
  34. Wang, Y., Deng, Q., Fractal Derivative Model for Tsunami Travelling, Fractals, 27 (2019), 1, 1950017
  35. He, J. H., A Simple Approach to One-Dimensional Convection-Diffusion Equation and Its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), Dec., ID 113565
  36. He, J. H., Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves, J. Appl. Comput. Mech., 6 (2020), 4, pp. 739-740
  37. Li, X. J., He, J. H., Variational Multi-Scale Finite Element Method for the Twophase Flow of Polymer Melt Filling Process, International Journal of Numerical Methods for Heat & Fluid Flow, Online first,
  38. 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
  39. Wang, K. L., et al., A Fractal Variational Principle for the Telegraph Equation with Fractal Derivatives, Fractals, On-line first,, 2020
  40. Ban, T., Cui, R. Q., He's Homotopy Perturbation Method for Solving Time Fractional Swift-Hohenberg Equation, Thermal science, 22 (2018), 4, pp. 1604-1605

© 2020 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, 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