numerical solution conditions idea Numerical solution of fractional differential equations with Caputo derivative by using numerical fractional predict–correct technique study 2022-03-18 convergence analysis Applied Sciences Caputo fractional order account values 26 main objective competencies axis equations numerical examples importance Caputo derivative operator true medicine operators articles objective cases order derivatives technique fractional differential equations real axis analysis Fractional differential equations have recently demonstrated their importance in a variety of fields, including medicine, applied sciences, and engineering. The main objective of this study is to propose an Adams-type multistep method for solving differential equations of fractional order. The method is developed by implementing the Lagrange interpolation and taking into account the idea of the Adams–Moulton method for fractional case. The fractional derivative applied in this study is in the Caputo derivative operator. The analysis of the proposed method is presented in terms of order of the method, order of accuracy, and convergence analysis, with the proposed method being proved to converge. The stability of the method is also examined, where the stability regions appear to be symmetric to the real axis for various values of α. In order to validate the competency of the proposed method, several numerical examples for solving linear and nonlinear fractional differential equations are included. The method will be presented in the numerical predict–correct technique for the condition where α∈(0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha \in (0,1)$\end{document}, in which α represents the order of fractional derivatives of Dαy(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D^{\alpha }y(t)$\end{document}. Lagrange interpolation terms of order multistep methods region nonlinear fractional differential equations Adams-Moulton method variety of fields 2022-03-18 terms 2022-09-02T16:08 example differential equations https://scigraph.springernature.com/explorer/license/ https://doi.org/10.1186/s13662-022-03697-6 fractional derivative fractional case interpolation variety accuracy field stability derivative operator method stability region order of accuracy article engineering science solution Springer Nature - SN SciGraph project Nur Amirah Zabidi Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia 1 Numerical and Computational Mathematics 10.1186/s13662-022-03697-6 doi Majid Zanariah Abdul 1687-1839 2731-4235 Advances in Continuous and Discrete Models Springer Nature Zarina Bibi Ibrahim dimensions_id pub.1146389211 2022 Adem Kilicman Mathematical Sciences