Study of renewable systems based on functional operators with shift

Karelin, Oleksandr; Gonzalez-Hernandez, Manuel; Hernández-Romero, Norberto; Seck-Tuoh-Mora, Juan Carlos

doi:10.12988/ams.2015.510622

Cited by 4 publications

(1 citation statement)

References 6 publications

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“…When we were modelling systems with renewable resources, Tarasenko, A., et al (2010), Karelin, O., et al (2015), , Karelin, O., et al (2018), we actively used functional operators with shift and related equations. Applications to economic and environmental problems were discussed .…”

Section: Introductionmentioning

confidence: 99%

On the solution of linear functional two-term equations with shift

Karelin,

Tarasenko

2023

ICBI

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This work is dedicated to the study of linear functional equations with shift in Hölder space. Previously, for such operators, conditions for invertibility were found and the inverse operator was constructed by the authors. The operators are used in modeling systems with renewable resources. Here we propose another approach to solving functional equations with shift. With the help of an algorithm, the initial equation is reduced to the first iterated equations, then to the second iterated equation. Continuing this process, we obtain the n-th iterated equation and the limit iterated equation. We prove the theorem on the equivalence of the original and the iterated equations. Based on the analysis of the solvability of the limit equation, we find a solution to the original equation. The solution is the sum of an infinite product and a functional series. The results, and the methods for obtaining them, are transparent and not as cumbersome compared to previous works.

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Section: Introductionmentioning

confidence: 99%

On the solution of linear functional two-term equations with shift

Karelin,

Tarasenko

2023

ICBI

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Study of Changes of the Individual Parameter of Resources in the Modelling of Renewable Systems

Karelin

Tarasenko

Barabash³

et al. 2019

Transactions on Engineering Technologies

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Modelling of Systems with Elements in Several States

Tarasenko

Karelin

Hernández

et al. 2021

Wseas Transactions on Environment and Development

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In this paper, we consider systems with one resource, which can be in several states. The states differ significantly in their processes of mortality, reproduction and mutual influence. For instance, infected elements can have a higher mortality rate than healthy and recovered ones. For cyclic models, in which the initial state of the system coincides with the final state, balance relations are found. They represent a system with functional operators with shift and integrals with degenerate kernels. Modified Fredholm method, proposed in previous works to solve the integral equations of the second type with degenerate kernels and shifts, is applied. Equilibrium position of a system with a three-state resource is found.

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Study of renewable systems based on functional operators with shift

Cited by 4 publications

References 6 publications

On the solution of linear functional two-term equations with shift

On the solution of linear functional two-term equations with shift

Study of Changes of the Individual Parameter of Resources in the Modelling of Renewable Systems

Modelling of Systems with Elements in Several States

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