Approximations of the Fractional Integral and Numerical Solutions of Fractional Integral Equations

摘要

In the present paper,we derive the asymptotic expansion formula for the trapezoidal approximation of the fractional integral.We use the expansion formula to obtain approxi-mations for the fractional integral of orders α,1+α,2+α,3+α and 4+α.The approxi-mations are applied for computation of the numerical solutions of the ordinary frac-tional relaxation and the fractional oscillation equations expressed as fractional integral equations.