Fractional oscillator equation: analytical solution and algorithm for its approximate computation

Abstract

In this paper the fractional oscillator equation in a finite time interval is considered. The fractional equation with derivatives of order $α \in (0, 1]$ is transformed into its corresponding integral form, by using the symbolic calculus method, in which the binomial expansion of the inverse integral operator is used. A new fractional integral operator is introduced. A numerical algorithm to approximate the solution of the considered equation is proposed. In the final part of this paper examples of numerical solutions of this equation are given.

Keywords

Fractional oscillator equation fractional Euler–Lagrange equation fractional integral equation numerical algorithm

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