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Analytic Resolving Families of Operators for Linear Equations with Hilfer Derivative
Journal of Mathematical Sciences, 2023In this research, Cauchy type problem for the fractional-order linear abstract differential equations with the Hilfer derivative is studied in Banach space. A criterion for the existence of exponentially bounded analytic resolving families of operators in terms of their resolvent operator is proposed.
Fedorov, Vladimir +2 more
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Strongly Continuous Resolving Families of Operators for Equations with a Fractional Derivative
Lobachevskii Journal of Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fedorov, V. E., Skorynin, A. S.
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Uniform stability of a family of resolvent operators in Hilbert spaces
Semigroup Forum, 2021In this paper, the authors consider two results on the uniform stability of a resolvent family \(\{R_h(t)\}_{t\geq 0}\), depending on a parameter \(h\). The first result is an extension of the Gearhart-Greiner-Pruss theorem on the resolvent family \(\{R_h(t)\}_{t\geq 0}\) and the authors provide some sufficient conditions on the uniform stability of \(\
Zhu, Shouguo, Fan, Zhenbin, Li, Gang
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Almost exponential stability and exponential stability of resolvent operator families
Semigroup Forum, 2016A new concept of almost exponential stability of the resolvent operator family \(\{ R(t), \, t\geq 0 \},\) \[ R(t) x = x+ \int_0^t a(t-\tau) A R(\tau) x\,d\tau, \, x\in {\mathcal D}(A),\quad A: {\mathcal D}(A ) \subseteq X\rightarrow X \] is constructed.
Fan, Zhenbin, Dong, Qixiang, Li, Gang
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Analytic in a Sector Resolving Families of Operators for Degenerate Evolution Fractional Equations
Journal of Mathematical Sciences, 2017Summary: We introduce a class of pairs of operators defining a linear homogeneous degenerate evolution fractional differential equation in a Banach space. Reflexive Banach spaces are represented as the direct sums of the phase space of the equation and the kernel of the operator at the fractional derivative.
Fedorov, V. E. +2 more
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