Numerical solution of fractional differential equations with Caputo derivative by using numerical fractional predict–correct technique

Abstract Fractional differential equations have recently demonstrated their importance in a variety of fields, including medicine, applied sciences, and engineering. The main objective this study is to propose an Adams-type multistep method for solving fractional order. developed by implementing the Lagrange interpolation taking into account idea Adams–Moulton case. derivative Caputo operator. analysis proposed presented terms order method, accuracy, convergence analysis, with being proved converge. stability also examined, where regions appear be symmetric real axis various values ? . In validate competency several numerical examples linear nonlinear are included. will predict–correct technique condition $\alpha \in (0,1)$ ? ? ( 0 , 1 ) , which represents derivatives $D^{\alpha }y(t)$ D y t