On a nonlinear Volterra integrodifferential equation involving fractional derivative with Mittag-Leffler kernel

Caraballo, Tomás; Ngoc, Tran Bao; Tuan, Nguyen Huy; Wang, Renhai

doi:10.1090/proc/15472

On a nonlinear Volterra integrodifferential equation involving fractional derivative with Mittag-Leffler kernel
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by Tomás Caraballo, Tran Bao Ngoc, Nguyen Huy Tuan and Renhai Wang PDF

Proc. Amer. Math. Soc. 149 (2021), 3317-3334 Request permission

Abstract:

In this paper, we study a nonlinear time-fractional Volterra equation with nonsingular Mittag-Leffler kernel in Hilbert spaces. By applying the properties of Mittag-Leffler functions and the method of eigenvalue expansion, we give a mild solution of our problem. Our main tool here is using some Sobolev embeddings.

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