A NEW NUMERICAL METHOD FOR SOLVING FRACTIONAL NEW NUMERICAL METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS IN THE SENSE OF CAPUTO-FABRIZIO DERIVATIVE

Abstract

In this paper, fractional differential equations in the sense of Caputo-Fabrizio derivative are transformed into integral equations. Then a high order numerical method for the integral equation is investigated by approximating the integrand with a piece-wise quadratic interpolant. The scheme is capable of handling both linear and nonlinear fractional differential equations. A detailed error analysis and stability region of the numerical scheme is rigorously established.