Applying Mikusiński's operational calculus to solve incommensurate systems involving Erdélyi–Kober derivatives

We investigate fractional differential equations and systems involving Erdélyi–Kober derivatives with several independent (incommensurate) fractional orders, and apply the method of Mikusiński to solve them using algebra. Our first contribution is to solve multi-term fractional differential equations involving arbitrarily many independent orders. Our main contribution is to solve coupled pairs of fractional differential equations involving two independent orders. In both cases, our solutions are expressed in terms of multivariate Mittag-Leffler functions.