We use waveform relaxation (WR) method to solve numerically fractional neutral functional differential equations and mainly consider the convergence of the numerical method with the help of a generalized Volterra-integral operator associated with the Mittag–Leffler function. We first give some properties of the integral operator. Using the proposed properties, we establish the convergence condition of the numerical method. Finally, we provide a new way to prove the convergence of waveform relaxation method for integer-order neutral functional differential equation, which is a special case of fractional neutral functional differential equation. Compared to the existing proof in the literature, our proof is concise and original.
Numerical Analysis of Fractional Neutral Functional Differential Equations Based on Generalized Volterra-Integral Operators
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 2, 2016; final manuscript received November 10, 2016; published online January 11, 2017. Assoc. Editor: Dumitru Baleanu.
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Ding, X., and Nieto, J. J. (January 11, 2017). "Numerical Analysis of Fractional Neutral Functional Differential Equations Based on Generalized Volterra-Integral Operators." ASME. J. Comput. Nonlinear Dynam. May 2017; 12(3): 031018. https://doi.org/10.1115/1.4035267
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