Mellin transform approach for the solution of coupled systems of fractional differential equations

•We find the solution of coupled systems of fractional different equations by using Mellin transform.•The shift in the argument of the transformed fractional operators is overcame.•Solution is found by solving an algebraic set of linear equations.

In this paper, the solution of a multi-order, multi-degree-of-freedom fractional differential equation is addressed by using the Mellin integral transform. By taking advantage of a technique that relates the transformed function, in points of the complex plane differing in the value of their real part, the solution is found in the Mellin domain by solving a linear set of algebraic equations. The approximate solution of the differential (or integral) equation is restored, in the time domain, by using the inverse Mellin transform in its discretized form.