Impulsive Fractional Differential Inclusions and Almost Periodic Waves

Stamov, Gani; Stamova, Ivanka

doi:10.3390/math9121413

Open AccessArticle

Impulsive Fractional Differential Inclusions and Almost Periodic Waves

by

Gani Stamov

^† and

Ivanka Stamova

^*,†

Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2021, 9(12), 1413; https://doi.org/10.3390/math9121413

Submission received: 28 May 2021 / Revised: 14 June 2021 / Accepted: 16 June 2021 / Published: 18 June 2021

(This article belongs to the Special Issue Qualitative Theory of Fractional-Order Systems)

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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.

Keywords: fractional differential inclusions; impulses; almost periodicity; fixed point; Hausdorff measure of noncompactness

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MDPI and ACS Style

Stamov, G.; Stamova, I. Impulsive Fractional Differential Inclusions and Almost Periodic Waves. Mathematics 2021, 9, 1413. https://doi.org/10.3390/math9121413

AMA Style

Stamov G, Stamova I. Impulsive Fractional Differential Inclusions and Almost Periodic Waves. Mathematics. 2021; 9(12):1413. https://doi.org/10.3390/math9121413

Chicago/Turabian Style

Stamov, Gani, and Ivanka Stamova. 2021. "Impulsive Fractional Differential Inclusions and Almost Periodic Waves" Mathematics 9, no. 12: 1413. https://doi.org/10.3390/math9121413

APA Style

Stamov, G., & Stamova, I. (2021). Impulsive Fractional Differential Inclusions and Almost Periodic Waves. Mathematics, 9(12), 1413. https://doi.org/10.3390/math9121413

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Impulsive Fractional Differential Inclusions and Almost Periodic Waves

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