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Matematicheskie Zametki, 2018, Volume 104, Issue 1, paper published in the English version journal
(Mi mzm12160)
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This article is cited in 8 scientific papers (total in 8 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.
Received: 13.12.2016 Revised: 11.12.2017
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
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https://www.mathnet.ru/eng/mzm12160
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