fractional integro-differential equation; Laguerre derivatives; Mittag-Leffler function; multinomial Mittag-Leffler function

In this paper we study explicit solutions of fractional integro-differential equations with variable coefficients involving Prabhakar-type operators. Analytic solutions to equations involving Prabhakar operators and Laguerre derivatives are obtained by means of operational methods. Cauchy type problems for fractional integro-differential equations of Volterra type with generalized Riemann-Liouville derivative operator, which contain generalized Mittag-Leffler function in the kernel are also considered. Using the Laplace transform method, explicit solutions of the fractional integro-differential equations of Volterra type with variable coefficients, proposed by Srivastava and Tomovski in [28] are established in terms of the multinomial Wright function.