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Mat. Zametki, 2018, Volume 104, Issue 1, paper published in the English version journal (Mi mz12160)  

This article is cited in 5 scientific papers (total in 5 papers)

Papers published in the English version of the journal

Stability Analysis of Distributed-Order Hilfer–Prabhakar Systems Based on Inertia Theory

M. Mashoof, A. H. Refahi Sheikhani, H. Saberi Najafi

Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, 1616 Iran

Abstract: The notion of a distributed-order Hilfer–Prabhakar derivative is introduced, which reduces in special cases to the existing notions of fractional or distributed-order derivatives. The stability of two classes of distributed-order Hilfer–Prabhakar differential equations, which are generalizations of all distributed or fractional differential equations considered previously, is analyzed. Sufficient conditions for the asymptotic stability of these systems are obtained by using properties of generalized Mittag-Leffler functions, the final-value theorem, and the Laplace transform. Stability conditions for such systems are introduced by using a new definition of the inertia of a matrix with respect to the distributed-order Hilfer–Prabhakar derivative.

Keywords: inertia, distributed-order Hilfer–Prabhakar derivative, stability.


English version:
Mathematical Notes, 2018, 104:1, 74–85

Bibliographic databases:

Received: 13.12.2016
Revised: 11.12.2017
Language:

Citation: M. Mashoof, A. H. Refahi Sheikhani, H. Saberi Najafi, “Stability Analysis of Distributed-Order Hilfer–Prabhakar Systems Based on Inertia Theory”, Math. Notes, 104:1 (2018), 74–85

Citation in format AMSBIB
\Bibitem{MasRefSab18}
\by M.~Mashoof, A.~H.~Refahi Sheikhani, H.~Saberi Najafi
\paper Stability Analysis
of Distributed-Order Hilfer–Prabhakar Systems
Based on Inertia Theory
\jour Math. Notes
\yr 2018
\vol 104
\issue 1
\pages 74--85
\mathnet{http://mi.mathnet.ru/mz12160}
\crossref{https://doi.org/10.1134/S000143461807009X}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3868960}
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\elib{https://elibrary.ru/item.asp?id=38754779}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054479405}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Sh. Eshaghi, R. Kh. Ghaziani, A. Ansari, “Stability and chaos control of regularized Prabhakar fractional dynamical systems without and with delay”, Math. Meth. Appl. Sci., 42:7 (2019), 2302–2323  crossref  isi  scopus
    2. P. Pirmohabbati, A. H. R. Sheikhani, H. S. Najafi, A. A. Ziabari, “Numerical solution of fractional mathieu equations by using block-pulse wavelets”, J. Ocean Eng. Sci., 4:4 (2019), 299–307  crossref  isi
    3. R. Zheng, F. Liu, X. Jiang, I. W. Turner, “Finite difference/spectral methods for the two-dimensional distributed-order time-fractional cable equation”, Comput. Math. Appl., 80:6 (2020), 1523–1537  crossref  mathscinet  zmath  isi
    4. P. Pirmohabbati, A. H. R. Sheikhani, H. S. Najafi, A. A. Ziabari, “Numerical solution of full fractional duffing equations with cubic-quintic-heptic nonlinearities”, AIMS Math., 5:2 (2020), 1621–1641  crossref  mathscinet  isi
    5. P. Pirmohabbati, A. H. R. Sheikhani, H. S. Najafi, A. A. Ziabari, “Numerical solution of strongly nonlinear full fractional duffing equation”, J. Interdiscip. Math., 23:8 (2020), 1531–1551  crossref  isi
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