Numerical solution of nonlinear fractionalRiccati differential equations usingcompact finite difference method

This paper aims to apply and investigate the compact finite differencemethods for solving integer-order and fractional-order riccati differentialequations. the fractional derivative in the fractional case is described inthe caputo sense. in solving the riccati equation, we first approximatefirst-order derivatives using the approach of compact finite difference. inthis way, the system of nonlinear equations is obtained, which solves thericcati equation. in addition, we examine the convergence analysis of theproposed approach for the fractional and nonfractional cases and prove thatthe methods are convergent under some suitable conditions. examples arealso given to illustrate the efficiency of our method compared to othermethods.