On the Existence and Uniqueness of a Fundamental Solution with Support in a Cone for a Multidimensional Wave Integro-Differential Operator with a Kernel Representable by Generalized Mittag-Leffler Functions

The properties of the fundamental solution to a linear Volterra integro-differential operator with partial derivatives are studied. The main part of this operator is a multidimensional wave operator perturbed by a convolution-type Volterra integral operator with a kernel representable as a sum of generalized Mittag-Leffler functions with positive coefficients. Integro-differential operators of this type arise in mathematical models of wave propagation in viscoelastic media and heat propagation in media with memory, and they have a number of other important applications. For the integro-differential operator under consideration, we prove the existence and uniqueness of a fundamental solution with support in the propagation cone of the corresponding multidimensional wave operator.