S-asymptotically $ \omega $-periodic mild solutions and stability analysis of Hilfer fractional evolution equations

Pallavi Bedi; Anoop Kumar; Thabet Abdeljawad; Aziz Khan

doi:10.3934/eect.2020089

Article Contents

2021, Volume 10, Issue 4: 733-748. Doi: 10.3934/eect.2020089

This issue Previous Article Lifespan of solutions to a parabolic type Kirchhoff equation with time-dependent nonlinearity Next Article Approximate controllability of network systems

S-asymptotically $ \omega $-periodic mild solutions and stability analysis of Hilfer fractional evolution equations

1.
Department of Mathematics and Statistics, Central University of Punjab, Bathinda, 151001, Punjab, India
2.
Department of Mathematics and General Sciences, Prince Sultan University, 66833, 11586 Riyadh, Saudi Arabia
3.
Department of Medical Research, China Medical University,40402, Taichung, Taiwan
4.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

^* Corresponding author
^* Corresponding author

Received: March 31, 2020

Revised: May 31, 2020

Early access: August 2020

Published: December 2021

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Abstract

In this article, we deal with the existence of S-asymptotically $ \omega $-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.

Keywords:

Hilfer fractional derivative,
S-asymptotically ω-periodic mild solutions,
Ulam-Hyers stability,
Ulam-Hyers-Rassias stability,
fixed point theory.

Mathematics Subject Classification: Primary: 26A33; Secondary: 34K45, 34A12, 47J35.

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