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