Explicit solutions for linear variable–coefficient fractional differential equations with respect to functions

Explicit solutions of differential equations complex fractional orders with respect to functions and continuous variable coefficients are established. The representations given in terms some convergent infinite series integro-differential operators, which can be widely efficiently used for analytic computational purposes. In the case constant coefficients, solution expressed multivariate Mittag-Leffler functions. particular, obtained result extends Luchko-Gorenflo representation formula [1, Theorem 4.1] a general class linear derivatives, derivatives function.