Closed-form solution for a mathematical extension of the multi-term fractional Bateman equations via Mikusiński operational method

Abstract

We give a closed-form solution, in terms of multivariate Mittag–Leffler functions, for a lower triangular linear fractional system consisting of Riemann–Liouville derivatives. For such a task, we use Mikusiński algebraic calculus, while solving a certain difference equation. The system is motivated by an extension of the multi-order fractional Bateman model in nuclear physics. Thus, the paper contributes to the theory of operational analysis in physics.