Generalized Riemann-Liouville Fractional Operators Associated with a Generalization of the Prabhakar Integral Operator

The paper introduces a new integral operator which generalizes the Prabhakar integral operator. The boundedness on the space of continuous functions and on the space of Lebesgue integrable functions on an interval is studied. In addition, the left inverse operator is constructed. The properties of composition with the k-Riemann-Liouville fractional operators are analized. Finally, as an application, a fractional generalization of the Cauchy problem associated with free electron laser equation is proposed.