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Fixed point approach for weakly asymptotic stability of fractional differential inclusions involving impulsive effects

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Abstract

We prove the global solvability and weakly asymptotic stability for a semilinear fractional differential inclusion subject to impulsive effects by analyzing behavior of its solutions on the half-line. Our analysis is based on a fixed point principle for condensing multi-valued maps, which is employed for solution operator acting on the space of piecewise continuous functions. The obtained results will be applied to a lattice fractional differential system.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02-2015.18.

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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

    Tran Dinh Ke

  2. Faculty of Computer Engineering and Science, Thuyloi University, 175 Tay Son, Dong Da, Hanoi, Vietnam

    Do Lan

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  1. Tran Dinh Ke
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  2. Do Lan
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Correspondence to Tran Dinh Ke.

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Ke, T.D., Lan, D. Fixed point approach for weakly asymptotic stability of fractional differential inclusions involving impulsive effects. J. Fixed Point Theory Appl. 19, 2185–2208 (2017). https://doi.org/10.1007/s11784-017-0412-6

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  • DOI: https://doi.org/10.1007/s11784-017-0412-6

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