Open AccessS-asymptotically $ \omega $-periodic mild solutions and stability analysis of Hilfer fractional evolution equations
Author(s) -
Pallavi Bedi,
Anoop Kumar,
Thabet Abdeljawad,
Aziz Khan
Publication year - 2021
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2020089
Subject(s) - banach space , mathematics , resolvent , omega , stability (learning theory) , interval (graph theory) , operator (biology) , fixed point , pure mathematics , space (punctuation) , mathematical analysis , combinatorics , physics , computer science , biochemistry , chemistry , repressor , quantum mechanics , machine learning , transcription factor , gene , operating system
In this article, we deal with the existence of S-asymptotically \begin{document}$ \omega $\end{document} -periodic mild solutions of Hilfer fractional evolution equations. We also investigate the Ulam-Hyers and Ulam-Hyers-Rassias stability of similar solutions. These results are established in Banach space with the help of resolvent operator functions and fixed point technique on an unbounded interval. An example is also presented for the illustration of obtained results.