Fractional wave equation with a frictional memory kernel of Mittag-Leffler type

In this paper we give an analytical treatment of a fractional wave equation with Caputo time fractional derivative and frictional memory kernel of Mittag-Leffler type. This problem generalizes a recently solved problem [62] of a wave equation for a vibrating string in presence of a fractional friction with power-law memory kernel. Such equations can be used in the context of modeling processes in complex and viscoelastic media.