Fractional differential equations: Ulam-Hyers stabilities
DOI:
https://doi.org/10.5540/03.2021.008.01.0415Palabras clave:
Fractional nonlinear abstract Cauchy, Ulam-Hyers stabilities, mild solution, Banach fixed point theorem.Resumen
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 will investigate the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of mild solutions of the fractional nonlinear abstract Cauchy problem in the intervals [0, T] and [0, oo) , by means of Banach’s fixed point theorem.
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