
Stability of mild solutions of the fractional nonlinear abstract Cauchy problem
Author(s) -
J. Vanterler da C. Sousa,
AUTHOR_ID,
Kishor D. Kucche,
E. Capelas de Oliveira,
AUTHOR_ID
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022015
Subject(s) - mathematics , fractional calculus , integer (computer science) , fixed point theorem , nonlinear system , cauchy distribution , stability (learning theory) , initial value problem , order (exchange) , banach space , path (computing) , differential equation , pure mathematics , mathematical analysis , computer science , physics , finance , quantum mechanics , machine learning , economics , programming language
Since the first work on Ulam-Hyers stabilities of differential equation solutions to date, many important and relevant papers have been published, both in the sense of integer order and fractional order differential equations. However, when we enter the field of fractional calculus, in particular, involving fractional differential equations, the path that is still long to be traveled, although there is a range of published works. In this sense, in this paper, we investigate the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of mild solutions for fractional nonlinear abstract Cauchy problem in the intervals $ [0, T] $ and $ [0, \infty) $ using Banach fixed point theorem.