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Approximate Controllability for a Class of Semi-Linear Fractional Integro-Differential Impulsive Evolution Equations of Order 1 < α < 2 with Delay

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  • Daliang Zhao

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

Abstract

This article is mainly concerned with the approximate controllability for some semi-linear fractional integro-differential impulsive evolution equations of order 1 < α < 2 with delay in Banach spaces. Firstly, we study the existence of the P C -mild solution for our objective system via some characteristic solution operators related to the Mainardi’s Wright function. Secondly, by using the spatial decomposition techniques and the range condition of control operator B , some new results of approximate controllability for the fractional delay system with impulsive effects are obtained. The results cover and extend some relevant outcomes in many related papers. The main tools utilized in this paper are the theory of cosine families, fixed-point strategy, and the Grönwall-Bellman inequality. At last, an example is given to demonstrate the effectiveness of our research results.

Suggested Citation

  • Daliang Zhao, 2023. "Approximate Controllability for a Class of Semi-Linear Fractional Integro-Differential Impulsive Evolution Equations of Order 1 < α < 2 with Delay," Mathematics, MDPI, vol. 11(19), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4069-:d:1247440
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    References listed on IDEAS

    as
    1. Yong Zhou, 2022. "Infinite Interval Problems for Fractional Evolution Equations," Mathematics, MDPI, vol. 10(6), pages 1-13, March.
    2. Ahmed Salem & Kholoud N. Alharbi & Hashim M. Alshehri, 2022. "Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space," Mathematics, MDPI, vol. 10(8), pages 1-17, April.
    3. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R. & Zhou, Yong, 2020. "A new approach on the approximate controllability of fractional differential evolution equations of order 1 < r < 2 in Hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R., 2020. "A new approach on approximate controllability of fractional evolution inclusions of order 1 < r < 2 with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. Lu, Liang & Liu, Zhenhai, 2015. "Existence and controllability results for stochastic fractional evolution hemivariational inequalities," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1164-1176.
    6. Mahmudov, N.I., 2020. "Finite-approximate controllability of semilinear fractional stochastic integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Kavitha, K. & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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