Solving Linear Coupled Fractional Differential Equations by Direct Operational Method and Some Applications

Abstract EN

A new direct operational inversion method is introduced for solving coupled linear systems of ordinary fractional differential equations.

The solutions so-obtained can be expressed explicitly in terms of multivariate Mittag-Leffler functions.

In the case where the multiorders are multiples of a common real positive number, the solutions can be reduced to linear combinations of Mittag-Leffler functions of a single variable.

The solutions can be shown to be asymptotically oscillatory under certain conditions.

This technique is illustrated in detail by two concrete examples, namely, the coupled harmonic oscillator and the fractional Wien bridge circuit.

Stability conditions and simulations of the corresponding solutions are given.