Fractional differential equations: Ulam-Hyers stabilities

J. Vanterler da C. Sousa, E. Capelas de Oliveira

Resumo


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.


Palavras-chave


Fractional nonlinear abstract Cauchy; Ulam-Hyers stabilities; mild solution; Banach fixed point theorem.

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Referências


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DOI: https://doi.org/10.5540/03.2021.008.01.0415

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