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FRACTIONAL DERIVATIVE OF INVERSE MATRIX AND ITS APPLICATIONS TO SOLITON THEORY

ABSTRACT
In this paper, a formula of the local fractional partial derivative of inverse matrix is presented and proved. With the help of the derived formula, two new non-linear PDE are derived including the local fractional non-isospectral self-dual Yang-Mills equation and the local fractional principal chiral field equation. It is shown that the formula of the local fractional partial derivative of inverse matrix can be used to derive some other local fractional non-linear PDE in soliton theory.
KEYWORDS
PAPER SUBMITTED: 2019-04-28
PAPER REVISED: 2019-08-29
PAPER ACCEPTED: 2019-08-29
PUBLISHED ONLINE: 2020-06-21
DOI REFERENCE: https://doi.org/10.2298/TSCI2004597Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE 4, PAGES [2597 - 2604]
REFERENCES
  1. Yang, X. J., et al., Local Fractional Integral Transforms and their Applications, Elsevier, London, UK, 2015
  2. Hu, Y., He, J. H, On Fractal Space-Time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 773-777
  3. Zhang, S., et al., Variable Separation Method for Nonlinear Time Fractional Biological Population Model, International Journal of Numerical Methods for Heat and Fluid Flow, 25 (2015), 7, pp. 1531-1541
  4. Zhang, S., Zhang, H. Q., Fractional Sub-Equation Method and its Applications to Non-linear Fractional PDE, Physics Letters A, 375 (2011), 7, pp. 1069-1073
  5. Zhang, S., et al., Exact Solutions of Time Fractional Heat-Like and Wave-Like Equations with Variable Coefficients, Thermal Science, 20 (2016), Suppl. 3, pp. S689-S693
  6. Vosika, Z. B., et al., Fractional Calculus Model of Electrical Impedance Applied to Human Skin, PLoS ONE, 8 (2013), 4, ID e59483
  7. Ain, Q. T., He, J. H., On Two-Scale Dimension And Its Applications, Thermal Science, 23 (2019), 3B, pp. 1707-1712
  8. He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Scence, 23 (2019), 4, pp. 2131-2133
  9. Zhang, W. F., A Velocity Extraction Method in Molecular Dynamic Simulation of Low Speed Nanoscale Flows, International Journal of Molecular Sciences, 7 (2006), 9, pp. 405-416
  10. He, J. H., Fractal Calculus and its Geometrical Explanation, Results Phys., 10 (2018), Sept., 272-276
  11. Wang, Q. L., et al., Fractal Calculus and its Application to Explanation of Biomechanism of Polar Bear Hairs, Fractals, 26 (2018), ID 1850086
  12. Wang, Q. L., et al., Fractal Calculus and its Application to Explanation of Biomechanism of Polar Bear Hairs (vol. 26, 1850086, 2018), Fractals, 27 (2019), 5, ID 1992001
  13. Wang Y., Deng, Q. G., Fractal Derivative Model for Tsunami Travelling, Fractals, 27 (2019), 1, ID 1950017
  14. 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
  15. Wang, Y., et al., A Fractal Derivative Model for Snow's Thermal Insulation Property, Thermal Science, 23 (2019), 4, pp. 2351-2354
  16. Wang, Y., et al., A Variational Formulation for Anisotropic Wave Traveling in a Porous Medium, Fractals, 27 (2019), 4, 1950047
  17. Wang, K. L., He, C. H. A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, ID 1950134
  18. Li, Y. S., Soliton and Integrable System (in Chinese), Shanghai Scientific and Technological Education Publishing House: Shanghai, China, 1991

© 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