226 research outputs found

    The Partial Averaging of Fuzzy Differential Inclusions on Finite Interval

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    The substantiation of a possibility of application of partial averaging method on finite interval for differential inclusions with the fuzzy right-hand side with a small parameter is considered

    Una nota sobre la existencia de soluciones para ecuaciones diferenciales difusas

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    Varios trabajos relacionados con la existencia y unicidad de soluciones para ecuaciones diferenciales difusas son basados en que el problema de Cauchy es equivalente a una ecuación integral. Este hecho que también es verdadero en el contexto clásico, no es siempre verdadero en el contexto de ecuaciones diferenciales difusas donde la derivada es considerada en el sentido generalizado. Mostraremos algunos ejemplos simples para demostrar esto y discutiremos sobre nuevas soluciones para una ecuación diferencial difusa

    Fuzzy Stochastic Differential Equations Driven by Semimartingales-Different Approaches

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    The first aim of the paper is to present a survey of possible approaches for the study of fuzzy stochastic differential or integral equations. They are stochastic counterparts of classical approaches known from the theory of deterministic fuzzy differential equations. For our aims we present first a notion of fuzzy stochastic integral with a semimartingale integrator and its main properties. Next we focus on different approaches for fuzzy stochastic differential equations. We present the existence of fuzzy solutions to such equations as well as their main properties. In the first approach we treat the fuzzy equation as an abstract relation in the metric space of fuzzy sets over the space of square integrable random vectors. In the second one the equation is interpreted as a system of stochastic inclusions. Finally, in the last section we discuss fuzzy stochastic integral equations with solutions being fuzzy stochastic processes. In this case the notion of the stochastic Itô’s integral in the equation is crisp; that is, it has single-valued level sets. The second aim of this paper is to show that there is no extension to more general diffusion terms

    List of contents and Author Index, Volume 19, 2006

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    Схема полного усреднения для нечетких дифференциальных включений на конечном промежутке

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    Наведено обґрунтування можливості застосування методу повного усереднення на скінченному проміжку для диференціальних включень із нечіткою правою частиною, які містять малий параметр.We justify the applicability of the method of complete averaging on a finite segment for differential inclusions with fuzzy right-hand sides containing a small parameter

    Simulation of Optimal Harvesting of Three Species Ecological Model with Closed Interval of Biological Parameter Using by Liapunov Function

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    The paper presents the study of three species ecological model with Prey N1, predator N2 and competitor to the Predator N3 and neutral with the predator N2 with imprecise biological parameters. The model is characterized by a set of first order nonlinear ordinary differential equations. Due to the lack of precise numerical information of the biological parameters such as prey population growth rate, predator population decay rate and predation coefficients, we consider the model with imprecise data as form of an interval in nature. Many authors have studied prey–predator harvesting model in different form, here we consider a simple prey–predator model under impreciseness and introduce parametric functional form of an interval and then study the model. Equilibrium points of the model are identified, the local stability is discussed using Routh - Hurwitz criteria and global stability by Liapunov function. The existence of bionomic equilibrium of the system has been discussed and optimal harvesting policy is given using Pontryagin’s maximum principle. The stability analysis is supported by Numerical simulation using Mat lab. Keywords: Prey; Predator; Competitor to the predator; Equilibrium points; interval number, Stability of the equilibrium points; Bionomic Equilibrium; Optimal harvesting policy; Pontryagin’s maximum principle; Numerical simulation using mat lab. DOI: 10.7176/IEL/9-1-0

    Fractional Calculus - Theory and Applications

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    In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications

    Simulation of Optimal Harvesting of Three Species Ecological Model with Closed Interval of Biological Parameter using by using First Order Nonlinear Ordinary Differential Equations

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    The paper presents the study of three species ecological model with Prey N1, predator N2 and competitor to the Predator N3 and neutral with the predator N2 with imprecise biological parameters. The model is characterized by a set of first order nonlinear ordinary differential equations. Due to the lack of precise numerical information of the biological parameters such as prey population growth rate, predator population decay rate and predation coefficients, we consider the model with imprecise data as form of an interval in nature. Many authors have studied prey–predator harvesting model in different form, here we consider a simple prey–predator model under impreciseness and introduce parametric functional form of an interval and then study the model. Equilibrium points of the model are identified, the local stability is discussed using Routh - Hurwitz criteria and global stability by Liapunov function. The existence of bionomic equilibrium of the system has been discussed and optimal harvesting policy is given using Pontryagin’s maximum principle. The stability analysis is supported by Numerical simulation using Mat lab. Keywords: Prey; Predator; Competitor to the predator; Equilibrium points; interval number, Stability of the equilibrium points; Bionomic Equilibrium; Optimal harvesting policy; Pontryagin’s maximum principle; Numerical simulation using mat lab. DOI: 10.7176/JAAS/52-0

    Усреднение импульсных дифференциальных включений с нечеткой правой частью

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    Наведено обґрунтування можливості застосування методу усереднення на скінченному проміжку до імпульсних диференціальних включень із нечіткою правою частиною, що містять малий параметр. Показано, що у випадку періодичних правих частин оцінку можна уточнити.We substantiate the possibility of application of the method of averaging on a finite interval to impulsive differential inclusions with fuzzy right-hand sides containing a small parameter. In the case of periodic right-hand sides, it is shown that the estimate can be improved

    Existence of solutions to Caputo fractional differential inclusions of 1<α<2 with initial and impulsive boundary conditions

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    This paper is concerned with the existence of solutions to the Caputo fractional differential inclusion of 1 < \alpha < 2 with initial and impulsive boundary conditions. A novel existence result is presented based on the fixed-point theorem of Dhage for multi-valued operators with some assumptions. Finally, two examples are provided to explicate the applicability of the main result
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