Higher-Order Numerical Solutions of the Fractional Relaxation-Oscillation Equation using Fractional Integration
arXiv:1603.087337 citationsh-index: 7
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It provides a numerical method for solving fractional differential equations, but the approach is incremental, extending known quadrature techniques.
The paper derives asymptotic expansions for trapezoidal approximations of fractional integrals and uses them to obtain numerical solutions of the fractional relaxation-oscillation equation with higher-order accuracy.
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 $α,1+α,2+α,3+α$ and $4+α$. The approximations are applied for computing the numerical solutions of the fractional relaxation-oscillation equation.