Delayed Langevin type equations with two fractional derivatives
Dynamical Systems
2019-07-04 v1 Classical Analysis and ODEs
Abstract
In this paper, we introduce a delayed Mittag-Leffler type function. With the help of the delayed Mittag-Leffler type functions, we give an explicit formula of solutions to linear nonhomogeneous fractional time-delay Langevin equations involving two Riemann-Liouville fractional derivatives. The existence and uniqueness of solutions are obtained by using an estimation of delayed Mittag-Leffler type functions in terms of exponential functions and a weighted norm via fixed point theorems. Further, we present Ulam--Hyers stability results.
Cite
@article{arxiv.1907.01746,
title = {Delayed Langevin type equations with two fractional derivatives},
author = {N. I. Mahmudov},
journal= {arXiv preprint arXiv:1907.01746},
year = {2019}
}