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    Wyświetlanie 1-9 z 9
    Tytuł:
    A numerical solution for a class of time fractional diffusion equations with delay
    Autorzy:
    Pimenov, V. G.
    Hendy, A. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/330624.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    fractional diffusion equation
    difference scheme
    convergence analysis
    równanie dyfuzji ułamkowe
    schemat różnicowy
    analiza zbieżności
    Opis:
    This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ 2−α + h4) in L ∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 477-488
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Investigation of Fixed-Point Computation Influence on Numerical Solutions of Fractional Differential Equations
    Autorzy:
    Piątek, P.
    Baranowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/386570.pdf
    Data publikacji:
    2011
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    równanie różniczkowe
    technika punktu stałego
    difference equation
    fixed point technique
    Opis:
    In this paper the problem of the influence of fixed point computation on numerical solutions of linear differential equations of fractional order is considered. It is a practically important problem, because of potential possibilities of using dynamical systems of fractional order in the tasks of control and filtering. Discussion includes numerical method is based on the Grünwald-Letnikov fractional derivative and how the application of fixed-point architecture influences its operation. Conclusions are illustrated with results of floating-point arithmetic with double precision and fixed point arithmetic with dif- ferent word lengths.
    Źródło:
    Acta Mechanica et Automatica; 2011, 5, 2; 101-107
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Problems in solving fractional differential equations in a microcontroller implementation of an FOPID controller
    Autorzy:
    Matusiak, Mariusz
    Ostalczyk, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/140935.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional calculus
    Grünwald-Letnikov fractional-order backward difference
    FOPID
    hardware implementation
    Opis:
    The article focuses on the fractional-order backward difference, sum, linear time-invariant equation analysis, and difficulties of the fractional calculus microcontroller implementation with regard to designing a fractional-order proportional integral derivative (FOPID) controller. In opposite to the classic proportional integral derivative (PID), the FOPID controller is defined by five independent parameters. Hence, it is more customizable and, potentially, more precise on condition that the values of fractional integration and differentiation orders are properly selected. However, a number of operations and the time required to calculate the output signal continuously increase. This can be a significant problem considering the limitations of a microcontroller, including memory size and a constant sampling time of the set-up analog-to-digital (ADC) converters. In the article, three solutions are considered, and results obtained in the experiments are presented.
    Źródło:
    Archives of Electrical Engineering; 2019, 68, 3; 565-577
    1427-4221
    2300-2506
    Pojawia się w:
    Archives of Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solutions of fractional nabla difference equations - existence and uniqueness
    Autorzy:
    Jonnalagadda, J. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255136.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nabla difference
    exponential function
    fixed point
    existence
    uniqueness
    continuous dependence
    Opis:
    In this article, we discuss existence, uniqueness and dependency of solutions of nonlinear fractional nabla difference equations in a Banach space equipped with a suitable norm, using the contractive mapping approach. As an application of the established results we present and analyse a few examples.
    Źródło:
    Opuscula Mathematica; 2016, 36, 2; 215-238
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the nonoscillatory behavior of solutions of three classes of fractional difference equations
    Autorzy:
    Grace, Said Rezk
    Alzabut, Jehad
    Punitha, Sakthivel
    Muthulakshmi, Velu
    Adiguzel, Hakan
    Powiązania:
    https://bibliotekanauki.pl/articles/255333.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Caputo difference operator
    nonoscillation criteria
    fractional difference equation mathematical inequalities
    Opis:
    In this paper, we study the nonoscillatory behavior of three classes of fractional difference equations. The investigations are presented in three different folds. Unlike most existing nonoscillation results which have been established by employing Riccati transfor mation technique, we employ herein an easily verifiable approach based on the fractional Taylor’s difference formula, some features of discrete fractional calculus and mathematical inequalities. The theoretical findings are demonstrated by examples. We end the paper by a concluding remark.
    Źródło:
    Opuscula Mathematica; 2020, 40, 5; 549-568
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of positive solutions to a discrete fractional boundary value problem and corresponding Lyapunov-type inequalities
    Autorzy:
    Chidouh, A.
    Torres, D. F. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255913.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional difference equations
    Lyapunov-type inequalities
    fractional boundary value problems
    positive solutions
    Opis:
    We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.
    Źródło:
    Opuscula Mathematica; 2018, 38, 1; 31-40
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Greens functions and existence of solutions of nonlinear fractional implicit difference equations with Dirichlet boundary conditions
    Autorzy:
    Cabada, Alberto
    Dimitrov, Nikolay D.
    Jonnalagadda, Jagan Mohan
    Powiązania:
    https://bibliotekanauki.pl/articles/29519501.pdf
    Data publikacji:
    2024
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional difference
    Dirichlet conditions
    Green’s function
    existence of solutions
    Opis:
    This article is devoted to deduce the expression of the Green’s function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional operators are applied, we are in presence of an implicit fractional difference equation. So, due to such a property, it is more complicated to calculate and manage the expression of the Green’s function than in the explicit case studied in a previous work of the authors. Contrary to the explicit case, where it is shown that the Green’s function is constructed as finite sums, the Green’s function constructed here is an infinite series. This fact makes necessary to impose more restrictive assumptions on the parameters that appear in the equation. The expression of the Green’s function will be deduced from the Laplace transform on the time scales of the integers. We point out that, despite the implicit character of the considered equation, we can have an explicit expression of the solution by means of the expression of the Green’s function. These two facts are not incompatible. Even more, this method allows us to have an explicit expression of the solution of an implicit problem. Finally, we prove two existence results for nonlinear problems, via suitable fixed point theorems.
    Źródło:
    Opuscula Mathematica; 2024, 44, 2; 167-195
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    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:
    Variation of constant formulas for fractional difference equations
    Autorzy:
    Anh, P. T.
    Babiarz, A.
    Czornik, A.
    Niezabitowski, M.
    Siegmund, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/229367.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional difference equation
    variation of constant
    separation of solutions
    Opis:
    In this paper, we establish variation of constant formulas for both Caputo and Riemann-Liouville fractional difference equations. The main technique is the Z-transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations.
    Źródło:
    Archives of Control Sciences; 2018, 28, 4; 617-633
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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