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1

On a first-order differential system with initial and nonlocal boundary conditions

Ngoc Le Thi Phuong, Long Nguyen Thanh

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

277--296

EN

This paper is devoted to the existence of solutions and the multiplicity of positive solutions of an initial-boundary value problem for a nonlinear first-order differential system with nonlocal conditions. The main tool is the fixed-point theorem in which we construct the novel representation of the associated Green’s functions with useful properties and define a cone in the Banach space suitably. Some examples are also given to demonstrate the validity of the main results.

2

A robust study of the transmission dynamics of zoonotic infection through non-integer derivative

Jan Rashid, Alharbi Asma, Boulaaras Salah, Alyobi Sultan, Khan Zaryab

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

922--938

EN

In Sub-Saharan Africa, zoonotic diseases are the leading cause of sickness and mortality, yet preventing their spread has long been difficult. Vaccination initiatives have significantly reduced the frequency of zoonotic diseases mostly in African regions. Nonetheless, zoonotic illnesses continue to be a hazard to underdeveloped countries. Zoonotic infections are spread by direct contact, food, and water. We construct an epidemic model to understand zoonotic disease transmission phenomena. The model is examined using the fundamental results of fractional theory. The reproduction parameter R0 was obtained by inspecting the model’s steady states. The stability of the system’s steady states has been demonstrated. The system’s reproduction parameter is quantitatively explored by varying various input parameters. Furthermore, the presence and uniqueness of the solution of the proposed dynamics of zoonotic diseases have been demonstrated. Different simulations of the recommended zoonotic disease model with different input factors are performed to inspect the complex dynamics of zoonotic disease with the influence of various model factors. To establish effective prevention and control measures for the infection, we analyse dynamical behaviour of the system. Decreasing the fractional order θ can decrease the infection level significantly. Different factors for reducing zoonotic diseases were recommended to regional policymakers.

3

On the solutions of a class of nonlinear functional integral quations in space C [0,a]

Özdemir İ., Çakan Ü.

Journal of Mathematics and Applications

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2015

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Vol. 38

105--114

EN

The principal aim of this paper is to give sufficient conditions for solvability of a class of some nonlinear functional integral equations in the space of continuous functions defined on interval [0,a]. The main tool used in our study is associated with the technique of measures of noncompactness. We give also some examples satisfying the conditions of our main theorem but not satisfying the conditions in [8].

4

Approximate controllability of the impulsive semilinear heat equation

Leiva H., Merentes N.

Journal of Mathematics and Applications

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2015

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Vol. 38

85--104

EN

In this paper we apply Rothe's Fixed Point Theorem to prove the interior approximate controllability of the following semilinear impulsive Heat Equation [...] where k = 1, 2, . . . , p, Ω is a bounded domain in [...] is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ω, the distributed control u belongs to [...]. Under this condition we prove the following statement: For all open nonempty subsets ω of Ω the system is approximately controllable on [0, τ]. Moreover, we could exhibit a sequence of controls steering the nonlinear system from an initial state z0 to an ϵ neighborhood of the nal state z1 at time τ > 0.

5

Monotonic continuous solution for a mixed type integral inclusion of fractional order

El-Sayed A. M. A., Al-Issa Sh. M.

Journal of Mathematics and Applications

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2010

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Vol. 33

27-34

EN

In this paper we are concerned with the mixed type integral inclusion [formula/wzór]. The existence of monotonic continuous solution will be proved. As an application the initial-value problem of the arbitrary (fractional) orders differential inclusion [formula/wzór] will be studied.

6

Fixed point theory for Volterra Kakutani Monch maps

Banaś J., O'Regan D.

Journal of Mathematics and Applications

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2008

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Vol. 30

33-41

EN

New fixed point theorems for multivalued Volterra Kakutani Mönch maps between Fréchet spaces are presented. The proof relies on fixed point theory in Banach spaces and viewing a Frechét space as the projective limit of a sequence of Banach spaces.