Higher-Order Numerical Solutions of the Fractional Relaxation-Oscillation Equation using Fractional Integration

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 order $\alpha ,1+\alpha ,2+\alpha ,3+\alpha$ and $4+\alpha$. The approximations are applied for computing the numerical solutions of the fractional relaxation-oscillation equation.

References in corpus (4)

• High-order Numerical Methods for Riesz Space Fractional Turbulent Diffusion Equation
• A survey on the Weierstrass approximation theorem
• A Second Order Approximation for the Caputo Fractional Derivative
• Three-Point Compact Approximation for the Caputo Fractional Derivative

Cited by in corpus (2)

• Approximations for the Caputo derivative (II)
• Fractional-compact numerical algorithms for Riesz spatial fractional reaction-dispersion equations