A new predictor–corrector method for fractional differential equations

We present a new predictor–corrector method to solve non-linear fractional differential equations involving Caputo derivative. The proposed method is compared with the fractional Adams method. Numerous illustrative examples discussed here demonstrate that the new method is more accurate and time efficient. A detailed error analysis given points to the higher accuracy of the new method. Furthermore the proposed method when applied to fractional analog of chaotic system introduced by Bhalekar and Daftardar-Gejji, unravels the underlying rich dynamics of the system.