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

Abstract

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 approximations for the fractional integral of orders $\alpha ,1+\alpha ,2+\alpha ,3+\alpha $ and $4+\alpha $. The approximations are applied for computation of the numerical solutions of the ordinary fractional relaxation and the fractional oscillation equations expressed as fractional integral equations.

Funding

Bulgarian National Science Fund(KP-06-M32/2)