A new family of predictor-corrector methods for solving fractional differential equations

Abstract

In the present paper, we propose a new family of six predictor-corrector methods to solve non-linear fractional differential equations (FDEs) of the form Dαy(t)=f(t,y(t)),0<α<1, where Dα denotes the αth order Caputo derivative and perform the stability and error analysis. Further, we extend these methods for solving systems of FDEs. The proposed methods have higher order accuracy and their execution time is drastically reduced as compared to existing methods such as fractional Adams method (FAM) and new predictor-corrector method (NPCM). They require only 10% of the time taken by FAM and 20% of the NPCM. Further, these methods converge for very small values of α when FAM and NPCM fail. We illustrate the applicability of the proposed methods by solving a variety of examples and some chaotic systems.