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

被引：10
作者：
Mashoof, M. [1 ]
Sheikhani, A. H. Refahi [1 ]
Najafi, H. Saberi [1 ]
机构：
[1] Islamic Azad Univ, Lahijan Branch, Fac Math Sci, Dept Appl Math, Lahijan 1616, Iran
来源：
MATHEMATICAL NOTES | 2018年 / 104卷 / 1-2期
关键词：
inertia; distributed-order Hilfer-Prabhakar derivative; stability; SMALLEST LARGEST EIGENVALUES; VECTOR ITERATION METHOD; PAIR;
D O I：
10.1134/S000143461807009X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：74 / 85
页数：12
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