Affiliation:
1. Faculty of Education, Thu Dau Mot University, Binh Duong Province, Vietnam
Abstract
In a Banach space, we consider the nonlinear Langevin time-delay
differential equations with ?-Caputo fractional derivatives. Using weighted
norms involving Mittag-Leffler functions, we obtain some existence and
uniqueness of solutions of the problem. Besides, in some cases, the
condition for the problem having a unique solution can be relaxed using
Burton?s method. We also obtain some Ulam-Hyers and Ulam-Hyers-Rassias
Mittag-Leffler stability results for the main equation. Two examples are
given to illustrate our theoretical findings.
Publisher
National Library of Serbia
Reference18 articles.
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