This paper proposes a three-point L1-based predictor–corrector scheme for the \(\psi \) -Caputo derivative. The L1-based rule and linear spline-based interpolation are utilized to perform the discretization of the derivative. The Daftardar-Gejji Jafari scheme (DGJ) is used to frame the iterative scheme. The error in the discretization procedure and the proposed approach is theoretically verified. The stability of the proposed approach is given in detail. Several numerical examples are solved to prove the numerical efficacy of the approach. An example is given by using the properties of the \(\psi \) -Caputo derivative to compare the proposed approach. Further, the computer virus model and the Chen system are simulated to demonstrate the method’s accuracy for a system of equations.
