Accuracy Analysis of the Numerical Solution of Linear Fractional-Order Differential Equations of Caputo Type Using the Predictor-Corrector Method - Haidari, Mohammad Jafar; Noori, Noorullah; Baidar, Abdul Wakil (Journal of Natural Sciences – Kabul University, 2025)
This paper investigates the accuracy of the Predictor–Corrector numerical method for solving linear differential equations with Caputo-type fractional derivatives. Fractional derivatives defined in the sense of Caputo are particularly important due to their ability to model memory and time-dependent behaviors in physical and engineering systems. The aim of this study is to evaluate the efficiency and accuracy of the Predictor–Corrector method in solving linear fractional differential equations. To achieve this, the structure of the method is first introduced, and then it is applied to several numerical examples, including both homogeneous and nonhomogeneous equations. The numerical results are compared with analytical solutions, and tables and comparative graphs are presented to assess the method's accuracy. The findings indicate that the Predictor–Corrector method provides reliable and accurate results and can be considered an effective approach for numerically solving linear fractional differential equations with classical initial conditions.