Results 1 to 10 of about 76,360 (233)

On Strongly Continuous Resolving Families of Operators for Fractional Distributed Order Equations [PDF]

Fractal and Fractional, 2021
The aim of this work is to find by the methods of the Laplace transform the conditions for the existence of a strongly continuous resolving family of operators for a linear homogeneous equation in a Banach space with the distributed Gerasimov–Caputo ...
Vladimir E. Fedorov, Nikolay V. Filin
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Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives

Mathematics, 2022
Some new necessary and sufficient conditions for the existence of analytic resolving families of operators to the linear equation with a distributed Riemann–Liouville derivative in a Banach space are established.
Vladimir E. Fedorov, Wei-Shih Du, Marko Kostić, Aliya A. Abdrakhmanova   +3 more
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Analytic Resolving Families for Equations with the Dzhrbashyan–Nersesyan Fractional Derivative

Fractal and Fractional, 2022
In this paper, a criterion for generating an analytic family of operators, which resolves a linear equation solved with respect to the Dzhrbashyan–Nersesyan fractional derivative, via a linear closed operator is obtained.
Vladimir E. Fedorov, Marina V. Plekhanova, Elizaveta M. Izhberdeeva   +2 more
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Integro-differential equations in Banach spaces and analytic resolving families of operators

Contemporary Mathematics. Fundamental Directions, 2023
We study a class of equations in Banach spaces with a Riemann–Liouville-type integro-differential operator with an operator-valued convolution kernel. The properties of \(k\)-resolving operators of such equations are studied and the class \(\mathcal A_{m,K,\chi}\) of linear closed operators is defined such that the belonging to this class is ...
Fedorov, V. E., Godova, A. D.
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Degenerate Multi-Term Equations with Gerasimov–Caputo Derivatives in the Sectorial Case

Mathematics, 2022
The unique solvability for the Cauchy problem in a class of degenerate multi-term linear equations with Gerasimov–Caputo derivatives in a Banach space is investigated.
Vladimir E. Fedorov, Kseniya V. Boyko
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Generators of Analytic Resolving Families for Distributed Order Equations and Perturbations

Mathematics, 2020
Linear differential equations of a distributed order with an unbounded operator in a Banach space are studied in this paper. A theorem on the generation of analytic resolving families of operators for such equations is proved.
Vladimir E. Fedorov
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Solvability of fractional differential inclusions with nonlocal initial conditions via resolvent family of operators [PDF]

International Journal of Nonlinear Sciences and Numerical Simulation, 2020
Abstract In this paper, we consider mild solutions to fractional differential inclusions with nonlocal initial conditions. The main results are proved under conditions that (i) the multivalued term takes convex values with compactness of resolvent family of operators; (ii) the multivalued term takes nonconvex values with compactness of ...
Yong-Kui Chang, Rodrigo Ponce, Xu-Sheng Yang   +2 more
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DUALITY THEORY OF REGULARIZED RESOLVENT OPERATOR FAMILY

Journal of Applied Analysis & Computation, 2011
Let \( k \in C(R^+)\), A be a closed linear densely defined operator in the Banach space \(X\) and \( \{R(t)\}_{t\geq 0} \) be an exponentially bounded \(k\)-regularized resolvent operator families generated by A. In this paper, we mainly study pseudo k-resolvent and duality theory of k-regularized resolvent operator families.
null Jizhou Zhang, null Yeping Li
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Inverse Problem for Evolutionary Equation with the Gerasimov – Caputo Fractional Derivative in the Sectorial Case

Известия Иркутского государственного университета: Серия "Математика", 2019
We investigates the unique solvability of a class of linear inverse problems with a time-independent unknown coefficient in an evolution equation in Banach space, which is resolved with respect to the fractional Gerasimov – Caputo derivative.
V.E. Fedorov, A. V. Nagumanova
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Threshold approximations with corrector for the resolvent of a factorized selfadjoint operator family [PDF]

St. Petersburg Mathematical Journal, 2006
In a Hilbert space we consider the family of operators admitting a factorization A(t) = X(t)∗X(t), where X(t) = X0 + tX1, t ∈ R. We suppose that the subspace N = KerA(0) is finite-dimensional. For the resolvent (A(t) + e2I)−1, we obtain an approximation in the operator norm on a fixed interval |t| ≤ t0 for small values of e. This approximation contains
M. Sh. Birman, T. A. Suslina
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