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.