Weak asymptotic stability for semilinear fractional differential equations with finite delays



	Weak asymptotic stability for semilinear fractional differential equations with finite delays


	Fixed Point Theory, Volume 22, No. 2, 2021, 837-854, July 1st, 2021 DOI: 10.24193/fpt-ro.2021.2.54 Authors: Nguyen Nhu Quan Abstract: This paper investigates a class of semilinear fractional differential equations with finite delays. Based on the α-resolvent theory, the fixed point theory for condensing maps and the local estimates of solutions, we prove the existence of solutions to the suggested system when the nonlinear part is superlinear. In the case, the nonlinear part is sublinear we study the weak asymptotic stability of the zero solution by applying a new Halanay type inequality. An application to a class of partial differential equations will be given. Key Words and Phrases: Weak asymptotic stability, Halanay inequality, measure of non-compactness, condensing map. 2010 Mathematics Subject Classification: 35B35, 37C75, 47H08, 47H10. Published on-line: July 1st, 2021. Abstract pdf Fulltext pdf Back to volume's table of contents