On Fractional Backward Differential Formulas Methods for Fractional Differential Equations with Delay
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In this paper, fractional backward differential formulas are presented for the numerical solution of fractional delay differential equations in Caputo sense. We focus on linear equations. Our investigation is focused on stability properties of the numerical methods and we determine stability regions for the fractional delay differential equations. Also we proposed the dependence of the solution on the parameters of the equation and conclude with a numerical treatment and examples based on the adaptation of a fractional backward differential formulas methods to the delay case. Numerical experiments are provided to illustrate potential and limitations of the different methods under investigation.
KeywordsFractional backward differential formulas Linear delay differential equations Stability
Mathematics Subject Classification34A30 65L06 65L20
The authors would like to express special thanks to the referees for carefully reading, constructive comments and valuable remarks which significantly improved the quality of this paper.
- 1.Podlubny, I.: Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Math. Sci. Eng. 198 (1999)Google Scholar
- 23.Zaky M.A.: An improved tau method for the multi-dimensional fractional Rayleigh–Stokes problem for a heated generalized second grade fluid. Comput. Math. Appl. (2017). https://doi.org/10.1016/j.camwa.2017.12.004
- 25.Zaky M.A.: A Legendre spectral quadrature tau method for the multi-term time-fractional diffusion equations. Comput. Appl. Math. 1–14 (2017). https://doi.org/10.1007/s40314-017-0530-1
- 26.Heris, M.S., Javidi, M.: Second order difference approximation for a class of Riesz space fractional advection-dispersion equations with delay (Submitted)Google Scholar
- 27.Heris, M.S., Javidi, M.: On fractional backward differential formulas method for differential equations of fractional order: applied to fractional order Rikitake system (Submitted)Google Scholar