On a variant of multivariate Mittag-Leffler's function arising in the Laplace transform method

By using the Laplace transform method, we revisit the multivariate Mittag-Leffler function as an effective tool to construct a solution for some classes of fractional differential equations with constant coefficients. To support our results, we discuss several particular cases related to classical fractional differential operators. The techniques are not only restricted to fractional derivative operators but also can be applied to general constant coefficient differential equations, including high-order ordinary differential equations.