AN ALGORITHM FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

We present and discuss an algorithm for the numerical solution of initial value problems of the form D y(t )= f(t,y(t)), y(0) = y0, where D y is the derivative of y of order in the sense of Caputo and 0 < 1. The algorithm is based on the fractional Euler's method which can be seen as a generalization of the classical Euler's method. Numerical examples are given and the results show that the present algorithm is very eective and convenient.