THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Bo Xu

,

Pengchao Shi

,

Yujin Zhang

,

Sheng Zhang

APPLICATION OF JORDAN CANONICAL FORM AND SYMPLECTIC MATRIX IN FRACTIONAL DIFFERENTIAL MODELS

ABSTRACT
Under consideration of this paper is the application of Jordan canonical form and symplectic matrix to two conformable fractional differential models. One is the new conformable fractional vector conduction equation which is reduced by using the Jordan canonical form of coefficient matrix and solved exactly, and the other is the new conformable fractional vector dynamical system with Hamilton matrix and symplectic matrix, which is derived by constructing the conformable fractional Euler-Lagrange equation and using fractional variational principle. It is shown that Jordan canonical form and symplectic matrix can be used to deal with some other conformable fractional differential systems in mathematical physics.
KEYWORDS
conformable fractional vector conduction equation, conformable fractional vector dynamical system, Jordan canonical form, symplectic matrix, Conformable fractional derivative
PAPER SUBMITTED: 2022-07-02
PAPER REVISED: 2022-09-15
PAPER ACCEPTED: 2022-10-01
PUBLISHED ONLINE: 2023-01-21
DOI REFERENCE: https://doi.org/10.2298/TSCI22S1019X
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special issue 1, PAGES [19 - 28]
REFERENCES
  1. Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, Cal., USA, 1999
  2. Inc, M., et al., Analysis of Novel Fractional COVID-19 Model with Real-Life Data Application, Results in Physics, 23 (2021), APR., ID 103968.
  3. Gulsen, S., Inc, M. Time Fractional Super KdV Equation: Lie Point Symmetries, Conservation Laws, Explicit Solutions with Convergence Analysis, International Journal of Geometric Methods in Modern Physics, 19 (2022), 8, ID 2250122
  4. Zhang, S., Zheng, X. W., Non-Differentiable Solutions for Non-Linear Local Fractional Heat Conduction Equation, Thermal Science, 25, (2021), Special Issue 2, pp. S309-S314
  5. Xu, B., et al., Analytical Methods for Non-Linear Fractional Kolmogorov-Petrovskii-Piskunov Equation: Soliton Solution and Operator Solution, Thermal Science, 25 (2021), 3B, pp. 2159-2166
  6. Xu, B., et al., Line Soliton Interactions for Shallow Ocean-Waves and Novel Solutions with Peakon, Ring, Conical, Columnar and Lump Structures Based on Fractional KP Equation, Advances in Mathematical Physics, 2021 (2021), ID 6664039
  7. Xu, B., et al., Variational Iteration Method for Two Fractional Systems with Boundary Conditions, Thermal Science, 26 (2022), 3B, pp. 2649-2657
  8. Xu, B., Zhang, S., Riemann-Hilbert Approach for Constructing Analytical Solutions and Conservation Laws of a Local Time-Fractional Non-Linear Schrödinger Equation, Symmetry, 13 (2021), 9, ID 13091593
  9. Khalil, R., et al., A New Definition of Fractional Derivative, Journal of Computational and Applied Mathematics, 264 (2014), JUL., pp. 65-70
  10. Zhang, S., Li, C. H., Method of Calculating a Kind of Up-Triangular Matrix Power, Journal of Jinzhou Normal College (Natural Science Edition), 23 (2001), 3, pp. 58-59. (in Chinese)
  11. ***, Former Algebra Group, Peking Univ., Advanced Algebra (in Chinese), 3rd ed., Higher Education Press, Beijing, CN, 2003
  12. Zhong W. X., Gao, Q., Symplectic Breaking the Cocoon ‒ Symplectic Expansion and New Level, Dalian University of Technology Press, Dalian, CN, 2011. (in Chinese)
  13. Zhao, S. J., An Expression of Symplectic Matrix on Fields, Journal of Heilongjiang Commercial College (Natural Sciences Edition), 15 (1999), 2, pp. 55-56. (in Chinese)
  14. Han, J., Long, Y., Normal Forms of Symplectic Matrices (II), Acta Scientiarum Naturalium Universitatis Nankaiensis, 31 (1999), 3, pp. 30-41
  15. Zhang, S., Notes and Modifications to the Calculation Method of Jordan Canonical Form (in Chinese), Journal of Bohai Univeristy (Natural Science Edition), 43 (2022), 2, pp. 155-16
  16. Qian, W. C., Generalized Variational Principle, Knowledge Publishing House, Shanghai, CN, 1985. (in Chinese)
  17. Ulutas, E., et al., Exact solutions of stochastic KdV equation with conformable derivatives in white noise environment, Thermal Science, 25 (2021), Special Issue 2, pp. S143-S149
  18. Yildirim, E. N., et al., Reproducing kernel functions and homogenizing transforms, Thermal Science, 25 (2021), Special Issue 2, pp. S9-S18
  19. Abdelrahman, M. A. E., et al., Exact solutions of the cubic Boussinesq and the coupled Higgs systems, Thermal Science, 24 (2020), Suppl. 1, pp. S333-S342
  20. Menni, Y., et al., Heat and mass transfer of oils in baffled and finned ducts, Thermal Science, 24 (2021), Suppl. 1, pp. S267-276
PDF VERSION [DOWNLOAD]
Application of Jordan canonical form and symplectic matrix in fractional differential models

© 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