On a nonlinear volterra integrodifferential equation involving fractional derivative with Mittag-Leffler Kernel

In this paper, a nonlinear time-fractional Volterra equation with nonsingular Mittag-Leffler kernel in Hilbert spaces is studied. By applying the properties of Mittag-Leffler functions and the method of eigenvalue expansion, the existence of a mild solution of our problem is proved. The main tool to prove our results is the use of some Sobolev embeddings