Abstract
Fractional order delay differential-algebraic equations have the characteristics of time lag and memory and constraint limit. These yield some difficulties in the theoretical analysis and numerical computation. In this paper, we are devoted to solving them by the waveform relaxation method. The corresponding convergence results are obtained, and some numerical examples show the efficiency of the method.
Highlights
Fractional delay differential-algebraic equations are composed of fractional delay differential equations and algebraic equations, and they are more accurate in describing some scientific and engineering problems with memory function and algebraic restrictions
For the fractional differential equations, the main works focus on obtaining the analytic solution, approximately analytical solution, and numerical solution
The fractional differential-algebraic equations have received much attention; the numerical methods in this field are still young; a few studies have been considered on the convergence of the numerical methods, such as variational iteration method, Adomian decomposition method, and fractional differential transform method [33, 34]
Summary
Fractional delay differential-algebraic equations are composed of fractional delay differential equations and algebraic equations, and they are more accurate in describing some scientific and engineering problems with memory function and algebraic restrictions. The fractional differential-algebraic equations have received much attention; the numerical methods in this field are still young; a few studies have been considered on the convergence of the numerical methods, such as variational iteration method, Adomian decomposition method, and fractional differential transform method [33, 34]. Ding and Jiang applied the WR method to solve fractional differential-algebraic equations and obtain the convergence results [35]. The variational iteration method for the fractional delay integrodifferential-algebraic equations has been studied in [36], but it is not suitable for long-time numerical calculation. In order to overcome this limitation, according to the characteristics of the problems, the discrete WR method is employed to solve the linear fractional delay differential-algebraic equations by constructing the efficient iterative method and obtain the convergence results which is much easier to achieve
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