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    Wyświetlanie 1-13 z 13
    Tytuł:
    On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms
    Autorzy:
    Graef, John R.
    Grace, Said R.
    Tune, Ercan
    Powiązania:
    https://bibliotekanauki.pl/articles/255164.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    integro-differential equations fractional differential equations nonoscillatory solutions boundedness
    Caputo derivative
    Opis:
    This paper is concerned with the asymptotic behavior of the nonoscillatory solutions of the forced fractional differential equation with positive and negative terms of the form [formula] where t ≥ c ≥ α ∈(0, 1), η ≥ 1 is the ratio of positive odd integers, and [formula] denotes the Caputo fractional derivative of y of order α. The cases [formula] are considered. The approach taken here can be applied to other related fractional differential equations. Examples are provided to illustrate the relevance of the results obtained.
    Źródło:
    Opuscula Mathematica; 2020, 40, 2; 227-239
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Mathematical Modeling of the Competition Between Acquired Immunity and Cancer
    Autorzy:
    Kolev, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/908160.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    medycyna
    matematyka
    leukemia
    acquired immunity
    immunotherapy
    antibodies
    integro-differential equations
    Opis:
    In this paper we propose and analyse a model of the competition between cancer and the acquired immune system. The model is a system of integro-differential bilinear equations. The role of the humoral response is analyzed. The simulations are related to the immunotherapy of tumors with antibodies.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2003, 13, 3; 289-296
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A nonlocal coagulation-fragmentation model
    Autorzy:
    Lachowicz, Mirosław
    Wrzosek, Dariusz
    Powiązania:
    https://bibliotekanauki.pl/articles/1208218.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    integro-differential equations
    diffusion
    coagulation
    nonlocal interaction
    fragmentation
    kinetic models
    Opis:
    A new nonlocal discrete model of cluster coagulation and fragmentation is proposed. In the model the spatial structure of the processes is taken into account: the clusters may coalesce at a distance between their centers and may diffuse in the physical space Ω. The model is expressed in terms of an infinite system of integro-differential bilinear equations. We prove that some results known in the spatially homogeneous case can be extended to the nonlocal model. In contrast to the corresponding local models the analysis can be carried out in the $L_1(Ω)$ setting. Our purpose is to study global (in time) existence, mass conservation and well-posedness of the model.
    Źródło:
    Applicationes Mathematicae; 2000, 27, 1; 45-66
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the semilinear integro-differential nonlocal Cauchy problem
    Autorzy:
    Majcher, Piotr
    Roszak, Magdalena
    Powiązania:
    https://bibliotekanauki.pl/articles/729610.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    integro-differential equations
    measure of weak non-compactness
    non-local problem
    Opis:
    In this paper, we prove an existence theorem for the pseudo-non-local Cauchy problem $x'(t) + Ax(t) = f(t,x(t),∫_{t₀}^{t} k(t,s,x(s))ds)$, x₀(t₀) = x₀ - g(x), where A is the infinitesimal generator of a C₀ semigroup of operator ${T(t)}_{t > 0}$ on a Banach space. The functions f,g are weakly-weakly sequentially continuous and the integral is taken in the sense of Pettis.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2005, 25, 1; 5-18
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A New Computational Method Based on Laguerre Polynomials for Solving Certain Nonlinear Partial Integro Differential Equations
    Autorzy:
    Gürbüz, B.
    Sezer, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/1031188.pdf
    Data publikacji:
    2017-09
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    nonlinear partial integro-differential equations
    Laguerre polynomials
    matrix and collocation methods
    error estimations
    Opis:
    In this study, we consider some nonlinear partial integro-differential equations. Most of these equations are used as mathematical models in many problems of physics, biology, chemistry, engineering, and in other areas. Our main purpose is to propose a new numerical method based on the Laguerre and Taylor polynomials, called matrix collocation method, for the numerical solution of the mentioned nonlinear equations under the initial or boundary conditions. To show the effectiveness of this approach, some examples along with error estimations are illustrated by tables and figures.
    Źródło:
    Acta Physica Polonica A; 2017, 132, 3; 561-563
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical modelling of the competition between the adaptive immune system and virus
    Autorzy:
    Kolev, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/206177.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    numerical modelling
    kinetic theory
    active particles
    integro-differential equations of Boltzmann type
    nonlinear dynamics
    virus
    adaptive immune system
    Opis:
    We present and analyze numerically a mathematical model of interactions between adaptive immune system and viral infection. The model is a bilinear system of partial integro-differential equations of Boltzmann type. It is a generalization of the recently proposed kinetic models that consider particular (namely, the cellmediated and the humoral) immune mechanisms used in the fight against viral infections. We use Matlab to solve complicated system of equations, present the results of computer simulations and explain their immunological meaning. The results show that the model can describe in a better way (in comparison with the previous kinetic models) real biological situations and is able to illustrate various methods of therapy.
    Źródło:
    Control and Cybernetics; 2011, 40, 3; 763-778
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Transients in Transformers with Non-Uniform Inductance and Capacitance Distributions
    Autorzy:
    Saied, M. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/262695.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie
    Tematy:
    distributed parameter circuits
    electromagnetic transients
    integro-differential equations
    modeling
    mutual parameters
    non-uniform
    power transformers
    transient response
    winding
    Opis:
    The electromagnetic transients in transformer windings exhibiting location–dependent inductances and capacitances are investigated in the time domain. Analytical functions describing this dependence are assumed and incorporated in the two integro–differential equations governing the transient voltage and current distributions. The boundary conditions are available from the source initiating the transients and the winding’s end termination. A numerical procedure is applied in order to get frequency domain solutions for the voltage and current in the form of Interpolating and Parametric Functions. The numerical Laplace inversion is then applied to these s–domain expressions. Results pertinent to transients initiated by step- and double-exponential impulse sources are presented and discussed. All possible transformers’ neutral connections are considered. The possible error introduced by neglecting either or both of the inductance and capacitance non-uniformities is addressed. Results indicate that the main error is attributed to neglecting the inductance non-uniformity, whereas the impact of the capacitance non-uniformity is relatively small. In most cases, the winding’s copper and insulation losses have a small effect on the transient response.
    Źródło:
    Electrical Power Quality and Utilisation. Journal; 2017, 20, 1; 7-14
    1896-4672
    Pojawia się w:
    Electrical Power Quality and Utilisation. Journal
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On some new phenomena in state-constrained optimal control if ODEs as well as PDEs are involved
    Autorzy:
    Pesch, H. J.
    Rund, A.
    Wahl, V.
    Wendl, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/969885.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control of partial differential equations
    ODE-PDE-constrained optimization
    state constraints
    non-local state-constraints
    integro-state constraints
    optimal control problems for integro-differential equations
    jump conditions
    Opis:
    In this paper we investigate a new class of optimal control problems with ODE as well as PDE constraints. We would like to call them "hypersonic rocket car problems", since they were inspired, on the one hand, by the well known rocket car problem from the early days of ODE optimal control, on the other hand by a recently investigated flight path trajectory optimization problem for a hypersonic aircraft. The hypersonic rocket car problems mimic the latter's coupling structure, yet in a strongly simplified form. They can therefore be seen as prototypes of ODE-PDE control problems. Due to their relative simplicity they allow to a certain degree to obtain analytical solutions and insights into the structure of the adjoints, which would currently be unthinkable with complex real life problems. Our main aim is to derive and verify the necessary optimality conditions. Most of the obtained results bear a lot of similarities with state constrained ODE optimal control problems, yet we also observed some new phenomena.
    Źródło:
    Control and Cybernetics; 2010, 39, 3; 647-660
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical solution of two-dimensional Fredholm integro-differential equations by Chebyshev integral operational matrix method
    Autorzy:
    Ishola, Christie Yemisi
    Taiwo, Omotayo Adebayo
    Adebisi, Ajimot Folasade
    Peter, Olumuyiwa James
    Powiązania:
    https://bibliotekanauki.pl/articles/2175510.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Chebyshev polynomials
    operational matrix
    two-dimensional
    Fredholm integro-differential equations
    wielomiany Czebyszewa
    macierz operacyjna
    modele dwuwymiarowe
    równanie całkowo-różniczkowe Fredholma
    Opis:
    This paper presents the Chebyshev Integral Operational Matrix Method (CIOMM) for the numerical solution of two-dimensional Fredholm Integro-Differential Equations (2D-FIDEs). The process of the method is obtaining the operational matrix of integration by evaluating a 2D integral of 2D Chebyshev polynomial basis functions and assuming approximate solutions of the 2D-FIDEs as a truncated 2D Chebyshev series. This leads to a system of linear algebraic equations which are solved to obtain the values of the unknown constants using Maple 18. Some numerical problems are solved to illustrate the practicability of the method.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 1; 29--40
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical study for a second order Fredholm integro-differential equation by applying Galerkin-Chebyshev-wavelets method
    Autorzy:
    Henka, Youcef
    Lemita, Samir
    Aissaoui, Mohamed-Zine
    Powiązania:
    https://bibliotekanauki.pl/articles/2202040.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Fredholm integro-differential equations
    nonlinear equation
    Galerkin method
    Chebyshev wavelets
    równanie całkowo-różniczkowe Fredholma
    równanie nieliniowe
    metoda Galerkina
    falki Czebyszewa
    Opis:
    In the present paper, we apply the Galerkin method using Chebyshev wavelets to approximate the exact solution for a second order Fredholm integro-differential equation with initial conditions. This numerical method gives us a nonlinear algebraic system that would be solved using the Picard successive approximations technique. Furthermore, we show the validity and the ability of the proposed method through some illustrative examples.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 4; 28--39
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solving linear Fredholm integro-differential equation by Nyström method
    Autorzy:
    Tair, Boutheina
    Guebbai, Hamza
    Segni, Sami
    Ghiat, Mourad
    Powiązania:
    https://bibliotekanauki.pl/articles/1839836.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Fredholm integral equation
    system of integral equations
    integro-differential equations
    Nyström method
    równanie całkowe Fredholma
    układ równań całkowych
    równanie całkowo-różniczkowe
    metoda Nyströma
    Opis:
    The study of the solution’s existence and uniqueness for the linear integro-differential Fredholm equation and the application of the Nyström method to approximate the solution is what we will present in this paper. We use the Neumann theorem to construct a sufficient condition that ensures the solution’s existence and uniqueness of our problem in the Banach space C1 [a,b]. We have applied the Nystrom method based on the trapezoidal ¨ rule to avoid adding other conditions in order to the approximation method’s convergence. The Nyström method discretizes the integro-differential equation into solving a linear system. Only with the existence and uniqueness condition, we show the solution’s existence and uniqueness of the linear system and the convergence of the numerical solution to the exact solution in infinite norm sense. We present two theorems to give a good estimate of the error. Also, to show the efficiency and accuracy of the Nyström method, some numerical examples will be provided at the end of this work.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 3; 53-64
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The implicit numerical method for the one-dimensional anomalous subdiffusion equation with a nonlinear source term
    Autorzy:
    Błasik, Marek
    Powiązania:
    https://bibliotekanauki.pl/articles/2086846.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional derivative
    fractional integral
    integro-differential equations
    numerical method
    finite difference method
    pochodna ułamkowa
    całkowanie ułamkowe
    równanie całkowo-różniczkowe
    metoda numeryczna
    metoda elementów skończonych
    Opis:
    In the paper, the numerical method of solving the one-dimensional subdiffusion equation with the source term is presented. In the approach used, the key role is played by transforming of the partial differential equation into an equivalent integro-differential equation. As a result of the discretization of the integro-differential equation obtained an implicit numerical scheme which is the generalized Crank-Nicolson method. The implicit numerical schemes based on the finite difference method, such as the Carnk-Nicolson method or the Laasonen method, as a rule are unconditionally stable, which is their undoubted advantage. The discretization of the integro-differential equation is performed in two stages. First, the left-sided Riemann-Liouville integrals are approximated in such a way that the integrands are linear functions between successive grid nodes with respect to the time variable. This allows us to find the discrete values of the integral kernel of the left-sided Riemann-Liouville integral and assign them to the appropriate nodes. In the second step, second order derivative with respect to the spatial variable is approximated by the difference quotient. The obtained numerical scheme is verified on three examples for which closed analytical solutions are known.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 6; e138240, 1--9
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Integro-differential equations on time scales with Henstock-Kurzweil delta integrals
    Autorzy:
    Sikorska-Nowak, Aneta
    Powiązania:
    https://bibliotekanauki.pl/articles/729234.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    integro-differential equations
    nonlinear Volterra integral equation
    time scales
    Henstock-Kurzweil delta integral
    HL delta integral
    Banach space
    fixed point
    measure of noncompactness
    Carathéodory solutions
    Opis:
    In this paper we prove existence theorems for integro - differential equations
    $x^Δ (t) = f(t,x(t),∫₀^t k(t,s,x(s))Δs)$,
    t ∈ Iₐ = [0,a] ∩ T, a ∈ R₊,
    x(0) = x₀
    where T denotes a time scale (nonempty closed subset of real numbers R), Iₐ is a time scale interval. Functions f,k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil delta integral, which generalizes the Henstock-Kurzweil integral.
    Additionally, functions f and k satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness. Moreover, we prove an Ambrosetti type lemma on a time scale.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 1; 71-90
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-13 z 13

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