THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Chun-Fu Wei

LOCAL FRACTIONAL HEAT AND WAVE EQUATIONS WITH LAGUERRE TYPE DERIVATIVES

ABSTRACT
In this paper, we investigate a local fractional PDE with Laguerre type derivative. The considered equation represents a general extension of the classical heat and wave equations. The method of separation of variables is used to solve the differential equation defined in a bounded domain.
KEYWORDS
Laguerre type derivatives, the method of separation of variables, local fractional derivative
PAPER SUBMITTED: 2018-12-26
PAPER REVISED: 2019-06-29
PAPER ACCEPTED: 2019-08-08
PUBLISHED ONLINE: 2020-06-21
DOI REFERENCE: https://doi.org/10.2298/TSCI2004575W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Issue 4, PAGES [2575 - 2580]
REFERENCES
  1. Wazwaz, A. M., Gorguis, A., Exact Solutions for Heat-Like and Wave-Like Equations with Variable Coefficients, Applied Mathematics and Computation, 149 (2004), 1, pp. 15-29
  2. Secer, A., Approximate Analytic Solution of Fractional Heat-Like and Wave-Like Equations with Variable Coefficients Using the Differential Transforms Method, Advances in Difference Equations, 48 (2012), 2, pp. 1-10
  3. Atangana, A., Exact Solutions Fractional Heat-Like and Wave-Like Equations with Variable Coefficients, Scientific Reports, 2 (2013), 2, pp. 1-5
  4. Yulita, M. R., et al., Variational Iteration Method for Fractional Heat- and Wave-Like Equations, Nonlinear Analysis Real World Applications, 10 (2009), 3, pp. 1854-1869
  5. 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
  6. Wei, C. F., Solving Time-Space Fractional Fitzhugh-Nagumo Equation by Using He-Laplace Decomposition Method, Thermal Science, 22 (2018), 4, pp. 1723-1728
  7. Yang, X. J., Baleanu, D., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method, Thermal Science, 2 (2013), 17, pp. 625-628
  8. Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
  9. Hu, Y., He, J. H., On Fractal Space-Time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 773-777
  10. He, J. H., A Tutorial Review on Fractal Space Time and Fractional Calculus, Int. J. Theor. Phys., 53, (2014), pp. 3698-718
  11. Karakas, M., Method of Separation of Variables, Linear Partial Differential Equations for Scientists and Engineers, 1 (2007), 1, pp. 231-272
  12. Rakhmelevich, I. V., On Application of the Variable Separation Method to Mathematical Physics Equations Containing Homogeneous Functions of Derivatives, Tomsk State University Journal of Mathematics and Mechanics, 2 (2013), 10, pp. 37-44
  13. Cação, I., et al., Laguerre Derivative and Monogenic Laguerre Polynomials: An Operational Approach, Mathematical and Computer Modelling, 5 (2011), 53, pp. 1084-1094
  14. Penson, K. A., et al., Laguerre-Type Derivatives: Dobinski Relations and Combinatorial Identities, Journal of Mathematical Physics, 8 (2009), 50, ID 083512
  15. He, J. H., Ji, F. Y., Taylor Series Solution for Lane-Emden Equation, Journal of Mathematical Chemistry, 57 (2019), 8, pp. 1932-1934
  16. Anjum, N., He, J. H., Laplace Transform: Making The Variational Iteration Method Easier, Applied Mathematics Letters, 92 (2019), June, pp. 134-138
  17. He, J. H., Some Asymptotic Methods For Strongly Nonlinear Equations, International Journal of Modern Physics B, 20 (2006), 10, pp. 1141-1199
  18. He, J. H., Homotopy Perturbation Technique, Computer Methods in Applied Mechanics and Engineering,. 178 (1999), 3-4, pp. 257-262
  19. He, J. H., A Coupling Method of a Homotopy Technique and a Perturbation Technique for Nonlinear Problems, International Journal of Non-Linear Mechanics., 35 (2000), 1, pp. 37-43
  20. He, J. H., Application of Homotopy Perturbation Method to Nonlinear Wave Equation, Chaos, Solitons and Fractals, 26 (2005), 3, pp. 695-700
  21. He, J. H., Homotopy Perturbation Method with an Auxiliary Term., Abstract and Applied Analysis, 2012 (2012), ID 857612
  22. He, J. H., Homotopy Perturbation Method with Two Expanding Parameters, Indian Journal of Physics, 88 (2014), 2, pp. 193-196
  23. Adamu, M. Y., Ogenyi, P. ,New Approach to Parameterized Homotopy Perturbation Method, Thermal Science , 22 (2018), 4, pp. 1865-1870
  24. Ban, T. Cui, R. Q., He's Homotopy Perturbation Method for Solving Time-Fractional Swift-Hohenerg Equation. Thermal Science, 22 (2018), 4, pp. 1601-1605
  25. 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
  26. Wu, Y., He, J. H., Homotopy Perturbation Method for Nonlinear Oscillators with Coordinate Dependent Mass., Results in Physics, 10 (2018), Sept., pp. 270-271
  27. Everitt, W. N., Kalf, H., The Bessel Differential Equation and the Hankel Transform, Journal of Computational and Applied Mathematics, 1 (2007), 208, pp. 3-19
  28. 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., 113565
  29. He, J. H., Ji, F.Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133
  30. Li, Z. B., et al., Exact Solutions of Time-Fractional Heat Conduction Equation by the Fractional Complex Transform, Thermal Science, 2 (2012), 16, pp. 335-338
  31. He, J. H., Fractal Calculus and Its Geometrical Explanation, Result in physics, 10 (2018), Sept., pp. 272-276
  32. Wang, Q. L., et al., Fractal Calculus and its Application to Explanation of Biomechanism of Polar Bear Hairs, Fractals, 26 (2018), 1850086
  33. Wang Y., Deng, Q. G., Fractal Derivative Model for Tsunami Travelling, Fractals, 27 (2019), 1, 1950017
  34. 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
  35. Ban, T., Cui, R. Q., He's Homotopy Perturbation Method for Solving Time Fractional Swift-Hohenberg Equations, Thermal science, 22 (2018), 4, pp. 1601-1605
  36. Wang, K. L., e .al., A Fractal Variational Principle for the Telegraph Equation with Fractal Derivatives, Fractals, On-line first, doi.org/10.1142/S0218348X20500589, 2020
  37. Wang, K. L., et al., Physical Insight of Local Fractional Calculus and its Application to Fractional Kdv-Burgers-Kuramoto Equation, Fractals, 27 (2019), 7 ID 1950122
PDF VERSION [DOWNLOAD]
Local fractional heat and wave equations with Laguerre type derivatives

© 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