Effect of perturbation in the numerical solution of fractional differential equations (Q1670356)

The authors deal with the following fractional initial value problem: \[ \begin{aligned} _{0}D_{t}^{\alpha}y(t) &= k(t)y(t)+f(t),\quad t\geq0, \\ y(0) &= y_{0}, \end{aligned}\tag{1} \] where \(0<\alpha<1\), \(_{0}D_{t}^{\alpha}\) stands for the Caputo fractional derivative of order \(\alpha\), \(k(t)\in C[0,+\infty)\) and \(f(t)\) is an appropriate function to reach the unique solution of the fractional initial value problem (1). The main approach of the paper is to identify the influence of some kind of perturbation on the exact and numerical solution of the initial value problem (1). In this study, the authors use the trapezoidal product integration methods on an uniform mesh to reach a numerical scheme of the unique solution of the fractional initial value problem (1).