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Impulsive Fractional Differential Inclusions and Almost Periodic Waves

Author

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  • Gani Stamov

    (Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
    These authors contributed equally to this work.)

  • Ivanka Stamova

    (Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
    These authors contributed equally to this work.)

Abstract

In the present paper, the concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo fractional derivative. New results on the existence and uniqueness are established by using the theory of operator semigroups, Hausdorff measure of noncompactness, fixed point theorems and fractional calculus techniques. Applications to a class of fractional-order impulsive gene regulatory network (GRN) models are proposed to illustrate the results.

Suggested Citation

  • Gani Stamov & Ivanka Stamova, 2021. "Impulsive Fractional Differential Inclusions and Almost Periodic Waves," Mathematics, MDPI, vol. 9(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1413-:d:577120
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    References listed on IDEAS

    as
    1. Gani Stamov & Ivanka Stamova, 2018. "Uncertain impulsive differential systems of fractional order: almost periodic solutions," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(3), pages 631-638, February.
    2. Wei-Shih Du & Marko Kostić & Manuel Pinto & Antonio Masiello, 2021. "Almost Periodic Functions and Their Applications: A Survey of Results and Perspectives," Journal of Mathematics, Hindawi, vol. 2021, pages 1-21, April.
    3. G. M. N’Guérékata & Marko Kostić, 2018. "Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions," Abstract and Applied Analysis, Hindawi, vol. 2018, pages 1-17, January.
    4. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    5. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    6. Yang, Xueyan & Peng, Dongxue & Lv, Xiaoxiao & Li, Xiaodi, 2019. "Recent progress in impulsive control systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 244-268.
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