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

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

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Revised: 11.12.2017
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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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000446511500009} \elib{http://elibrary.ru/item.asp?id=38754779} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054479405}