Open AccessOn a nonlinear Volterra integrodifferential equation involving fractional derivative with Mittag-Leffler kernel
Author(s) -
Tomás Caraballo,
Tran Bao Ngoc,
Nguyen Huy Tuan,
Renhai Wang
Publication year - 2021
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/15472
Subject(s) - invertible matrix , mathematics , mittag leffler function , fractional calculus , kernel (algebra) , sobolev space , nonlinear system , volterra integral equation , eigenvalues and eigenvectors , volterra equations , mathematical analysis , laplace transform , pure mathematics , integral equation , physics , quantum mechanics
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.