A Chebyshev pseudo spectral method for solving fractional differential equations

• Yazdani Cherati, AllahBakhsh ^[1] ; Kiasari, Morteza Mohammadnezhad ^[1]
  1. [1] University of Mazandaran

     University of Mazandaran

     Irán

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 3, 2020, págs. 711-720
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-03-0044
• Enlaces
  • Texto completo
• Resumen

  • The Chebyshev pseudo-spectral method is generalized for solving fractional differential equations with initial conditions. For this purpose, an appropriate representation of the solution is presented and the Chebyshev pseudo-spectral differentiation matrix of fractional order is derived. Then, by using Chebyshev pseudo-spectral scheme, the problem is reduced to the solution of a system of algebraic equations.

• Referencias bibliográficas
  • A. H. Bhrawy, “A new spectral algorithm for time-space fractional partial differential equations with subdiffusion and superdiffusion”, Proceedings...
  • R. Baltensperger and M. R. Trummer, “Spectral differencing with a twist”, SIAM journal on scientific computing, vol. 24, no. 5, pp. 1465–1487,...
  • K. Diethelm, The analysis of fractional differential equations: an application-oriented exposition using differential operators of Caputo...
  • D. Funaro, Polynomial approximation of differential equations. Berlin: Springer, 1992, doi: 10.1007/978-3-540-46783-0
  • W. Gautschi, Orthogonal polynomials: computation and approximation. New York, NY: Oxford University Press, 2004.
  • R. Hilfer, Ed., Applications of fractional calculus in physics. Singapore: World Scientific, 2000, doi: 10.1142/3779
  • J. T. Machado, V. Kiryakova, and F. Mainardi, “Recent history of fractional calculus”, Communications in nonlinear science and numerical simulation,...
  • F. Mainardi, “Fractional calculus”, in Fractals and fractional calculus in continuum mechanics, A. Carpinteri and F. Mainardi, Eds. Vienna:...
  • K. B. Oldham and J. Spanier, The fractional calculus: theory and applications of differentiation and integration to arbitrary order. New York...
  • I. Podlubny, Fractional differential equations. San Diego, CA: Elsevier, 1999. [On line]. Available: https://bit.ly/3gFpe3g
  • G. Szeg?, Orthogonal polynomials. Providence, RI: American Mathematical Society, 1939, doi: 10.1090/coll/023
  • B. D. Welfert, “Generation of pseudospectral differentiation matrices I”, SIAM Journal on numerical analysis, vol. 34, no. 4, pp. 1640–1657,...