THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Shao-Wen Yao

,

Kang-Le Wang

A NEW APPROXIMATE ANALYTICAL METHOD FOR A SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS

ABSTRACT
In this paper, a new approximate analytical method is established, and it is useful in constructing approximate analytical solution a system of fractional differential equations. The results show that our method is reliable and efficient for solving the fractional system.
KEYWORDS
caputo fractional derivative, analytical solution, fractional differential equations, DGJ method
PAPER SUBMITTED: 2018-06-13
PAPER REVISED: 2018-07-12
PAPER ACCEPTED: 2018-08-11
PUBLISHED ONLINE: 2019-04-14
DOI REFERENCE: https://doi.org/10.2298/TSCI180613120Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 3, PAGES [S853 - S858]
REFERENCES
  1. Daftardar, G. J., et al., An Iterative Method for Solving Nonlinear Functional Equations, Journal of Mathematical Analysis and Applications , 316(2006), 2, pp. 753-763
  2. Adomian, G., A Review of the Decomposition Method in Applied Mathematics, Journal of mathematical analysis and applications, 135 (1988), 2, pp. 501-544
  3. Elsaid, A., Fractional Differential Transform Method Combined with the Adomian Polynomials, Applied Mathematics and Computation, 218 (2012), 12, pp. 6899-6911
  4. Yang, X. J., et al., A New Computational Approach for Solving Nonlinear Local Fractional PDEs, Journal of Computational and Applied Mathematics, 339(2018), September, 285-296
  5. Yang, X. J., et al., On Exact Traveling-wave Solutions for Local Fractional Korteweg-de Vries Equation, Chaos, 26 (2016), 8, 084312
  6. Yang, X. J., et al., Exact Traveling-wave Solution for Local Fractional Boussinesq Equation in Fractal Domain, Fractals, 25(2017), 04, 1740006
  7. Yang, X. J., et al., Exact Travelling Wave Solutions for the Local Fractional Two-dimensional Burgers-type Equations, Computers & Mathematics with Applications, 73(2017), 2, pp.203-210
  8. Hashim, I., et al., Homotopy Analysis Method for Fractional IVPs, Communications in Nonlinear Science and Numerical Simulation, 14(2009), 3, pp. 674-684
  9. Sari, M., et al., A Solution to the Telegraph Equation by Using DGJ Method, International Journal of Nonlinear Science, 17 (2014), 1, pp. 57-66
  10. Daftardar, G. J., et al., Adomian Decomposition: a Tool for Solving a System of Fractional Differential Equations, Journal of Mathematical Analysis and Applications, 301(2005), 2, pp. 508-518
  11. Bhalekar, S., et al., New Iterative Method: Application to Partial Differential Equations, Applied Mathematics and Computation , 203(2008), 2, pp. 778-783
  12. Daftardar, G. J., et al., Solving Fractional Boundary Value Problems with Dirichlet Boundary Conditions Using a New Iterative Method, Computers & Mathematics with Applications , 59(2010), 5, pp. 1801-1809
  13. Yang, X. J. General Fractional Derivatives: Theory, Methods and Applications, New York: CRC Press, 2019
  14. Jafari, H., et al., Solving a System of Nonlinear Fractional Differential Equations Using Adomian Decomposition, Journal of Computational and Applied Mathematics , 196 (2006), 2, pp. 644-651
  15. Daftardar, G. V., et al., Analysis of a System of Nonautonomous Fractional Differential Equations Involving Caputo Derivatives, Journal of Mathematical Analysis and Applications , 328(2007), 2, pp. 1026-1033
  16. Wang, K. L., et al., A Modification of the Reduced Differential Transform Method for Fractional Calculus. Thermal Science, 22(2018), 4, pp. 1871-1875
  17. Edwards, J. T., et al., The Numerical Solution of Linear Multi-term Fractional Differential Equations: Systems of Equations, Journal of Computational and Applied Mathematics , 148(2002), 2, pp. 401-418
  18. Momani, S., et al., Numerical Solutions for Systems of Fractional Differential Equations by the Decomposition Method, Applied Mathematics and Computation , 162(2005), 3, pp. 1351-1365
  19. Wazwaz, A. M., The Decomposition Method Applied to Systems of Partial Differential Equations and to the Reaction-diffusion Brusselator Model, Applied Mathematics and Computation , 110 (2000), 2, pp. 251-264
  20. Hu, Y., et al., On Fractal Space-time and Fractional Calculus. Thermal Science, 20 (2016), 3, pp. 773-777
  21. Wazwaz, A. M., The Variational Iteration Method for Solving Linear and Nonlinear Systems of PDEs, Computers & Mathematics with Applications, 54(2007), 7, pp. 895-902
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A new approximate analytical method for a system of fractional differential equations

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