A new finite-difference predictor-corrector method for fractional differential equations

We present a new finite-difference predictor-corrector method (L1 - PCM) to solve nonlinear fractional differential equations (FDEs) along with its error and stability analysis. The method is further extended for systems of FDEs. The proposed method is applied to fractional version of chaotic system introduced by Bhalekar and Daftardar-Gejji to explore its rich dynamics. The proposed method is accurate, time-efficient and performs well even for very small values of the order of the derivatives.