Finite-Time Mittag-Leffler Stability of Fractional-Order Quaternion-Valued Memristive Neural Networks with Impulses

  • A. Pratap
  • R. Raja
  • J. Alzabut
  • J. Dianavinnarasi
  • J. CaoEmail author
  • G. Rajchakit


The finite-time Mittag-Leffler stability for fractional-order quaternion-valued memristive neural networks (FQMNNs) with impulsive effect is studied here. A new mathematical expression of the quaternion-value memductance (memristance) is proposed according to the feature of the quaternion-valued memristive and a new class of FQMNNs is designed. In quaternion field, by using the framework of Filippov solutions as well as differential inclusion theoretical analysis, suitable Lyapunov-functional and some fractional inequality techniques, the existence of unique equilibrium point and Mittag-Leffler stability in finite time analysis for considered impulsive FQMNNs have been established with the order \(0<\beta <1\). Then, for the fractional order \(\beta \) satisfying \(1<\beta <2\) and by ignoring the impulsive effects, a new sufficient criterion are given to ensure the finite time stability of considered new FQMNNs system by the employment of Laplace transform, Mittag-Leffler function and generalized Gronwall inequality. Furthermore, the asymptotic stability of such system with order \(1<\beta <2\) have been investigated. Ultimately, the accuracy and validity of obtained finite time stability criteria are supported by two numerical examples.


Quaternion-valued Memristor Fractional-order neural networks Finite-time stability 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Vel Tech High Tech Dr Rangarajan Dr Sakunthala Engineering CollegeChennaiIndia
  2. 2.Ramanujan Centre for Higher MathematicsAlagappa UniversityKaraikudiIndia
  3. 3.Department of Mathematics and General SciencesPrince Sultan UniversityRiyadhSaudi Arabia
  4. 4.School of MathematicsSoutheast UniversityNanjingChina
  5. 5.Department of Mathematics, Faculty of ScienceMaejo UniversityChiang MaiThailand

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