A NUMERICAL ALGORITHM TO INITIAL VALUE PROBLEM OF LINEAR CAPUTO FRACTIONAL-ORDER DIFFERENTIAL EQUATION

A numerical algorithm is presented to solve the initial value problem of linear Caputo fractional-order differential equations. Error analysis has been done to Taylor series algorithm, the reason has been found why the error of the algorithm is large, the condition of using Taylor series algorithm is presented. A new algorithm called exponential function algorithm is proposed based on the analysis. Nonzero initial value problem could be transformed into zero initial value problem. The obtained fractional order differential equation is transformed into difference equation, the numerical solution can be found with closed form solution formula. The error of the numerical solution can be modified with prediction-correction algorithm.