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...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 ordersα,1+α,2+α,3+αand 4+α.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.展开更多
基金This work was supported by the Bulgarian National Science Fund under Project KP-06-M32/2"Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics"。
文摘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 ordersα,1+α,2+α,3+αand 4+α.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.
