Convergence of Variational Iteration Method for Fractional Delay Integrodifferential‐Algebraic Equations

Abstract

Fractional order delay integrodifferential-algebraic equations are often used for many practical modeling problems in science and engineering, which have time lag, memory, constraint limit, and so forth. These yield some difficulties in numerical computation. The iterative methods are good choice. In the present paper, we construct variational iteration method for solving them by using the appropriate restricted variation. This overcomes the difficulties caused by limitations of large storage amount and algebraic constraint and extends the previous conclusions.

Chebyshev Neural Network Method for Solving Delay-Integro-Differential-Algebraic Equations Based on Variable Transformation

“…In formula (8), both matrix H and vector Y are known, only vector β is unknown, so equation ( 8) is a linear equation of a set of unknown parameters vector β. Obviously, this is equivalent to finding the least-squares solution of equation ( 8), i.e.…”

“…Reference [5] introduced the asymptotic stability of the Runge-Kutta method for linear DIDAEs. In addition, references [6][7][8] studied the convergence analysis of variational iteration method and waveform relaxation method for several kinds of DIDAEs. As we all know, the numerical methods constructed are generally subject to the strict requirements of step size, and the delay term and integral term will bring a lot of computation and lead to difficulties in solving.…”

Existence results for fractional delay integro-differential equations with multi-point boundary conditions

“…Shri Akiladevi and Balachandran [16] discussed the existence and uniqueness of solution to the fractional delay integrodifferential equations with four-point multiterm fractional integral boundary conditions. The fractional differential equations with delay has drawn the attention of researchers in the recent years, for detail we refer [1], [2], [3], [9], [18], [21]. Motivated by this consideration, in this paper, we shall discuss the existence and uniqueness of solutions for the fractional delay integrodifferential equations with multi-point boundary conditions of the form by using appropriate fixed point theorems:…”

Discrete Waveform Relaxation Method for Linear Fractional Delay Differential-Algebraic Equations

“…But it is difficult to verify convergence conditions. 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.…”