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    Wyświetlanie 1-5 z 5
    Tytuł:
    Quasilinearization method for finite systems of nonlinear RL fractional differential equations
    Autorzy:
    Denton, Zachary
    Ramirez, Juan Diego
    Powiązania:
    https://bibliotekanauki.pl/articles/1397341.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional differential systems
    lower and upper solutions
    quasilinearization method
    Opis:
    In this paper the quasilinearization method is extended to finite systems of Riemann-Liouville fractional differential equations of order 0 < q < 1. Existence and comparison results of the linear Riemann-Liouville fractional differential systems are recalled and modified where necessary. Using upper and lower solutions, sequences are constructed that are monotonic such that the weighted sequences converge uniformly and quadratically to the unique solution of the system. A numerical example illustrating the main result is given.
    Źródło:
    Opuscula Mathematica; 2020, 40, 6; 667-683
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multiple solutions of boundary value problems on time scales for φ-laplacian operator
    Autorzy:
    Amster, Pablo
    Kuna, Mariel Paula
    Santos, Dionicio Pastor
    Powiązania:
    https://bibliotekanauki.pl/articles/255690.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    dynamic equations on time scales
    nonlinear boundary value problems
    upper and lower solutions
    Leray-Schauder degree
    multiple solutions
    Opis:
    We establish the existence and multiplicity of solutions for some boundary value problems on time scales with a y-Laplacian operator. For this purpose, we employ the concept of lower and upper solutions and the Leray-Schauder degree. The results extend and improve known results for analogous problems with discrete p-Laplacian as well as those for boundary value problems on time scales.
    Źródło:
    Opuscula Mathematica; 2020, 40, 4; 405-425
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Monotone iterative technique for finite systems of nonlinear Riemann-,Lliouville fractional differential equations
    Autorzy:
    Denton, Z.
    Vatsala, A.S.
    Powiązania:
    https://bibliotekanauki.pl/articles/255746.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional differential systems
    coupled lower and upper solutions
    mixed quasimonotone property
    Opis:
    Comparison results of the nonlinear scalar Riemann-Liouville fractional differential equation of order q, 0 < q ≤ 1, are presented without requiring Hölder continuity assumption. Monotone method is developed for finite systems of fractional differential equations of order q, using coupled upper and lower solutions. Existence of minimal and maximal solutions of the nonlinear fractional differential system is proved.
    Źródło:
    Opuscula Mathematica; 2011, 31, 3; 327-339
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Monotone method for Riemann-Liouville multi-order fractional differential systems
    Autorzy:
    Denton, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/254754.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional differential systems
    multi-order systems
    lower and upper solutions
    monotone method
    Opis:
    In this paper we develop the monotone method for nonlinear multi-order N-systems of Riemann-Liouville fractional differential equations. That is, a hybrid system of nonlinear equations of orders qi where 0 < qi < 1. In the development of this method we recall any needed existence results along with any necessary changes. Through the method's development we construct a generalized multi-order Mittag-Leffler function that fulfills exponential-like properties for multi-order systems. Further we prove a comparison result paramount for the discussion of fractional multi-order inequalities that utilizes lower and upper solutions of the system. The monotone method is then developed via the construction of sequences of linear systems based on the upper and lower solutions, and are used to approximate the solution of the original nonlinear multi-order system.
    Źródło:
    Opuscula Mathematica; 2016, 36, 2; 189-206
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Monotone iterative methods for infinite systems of reaction-diffusion-convection equations with functional dependence
    Autorzy:
    Brzychczy, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/255097.pdf
    Data publikacji:
    2005
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    infinite systems
    reaction-diffusion-convection equations
    semilinear parabolic differential-functional equations
    Volterra functionals
    monotone iterative methods
    method of upper and lower solutions
    Opis:
    We consider the Fourier first initial-boundary value problem for an infinite system of semilinear parabolic differential-functional equations of reaction-diffusion-convection type of the form [formula] where [formula] in a bounded cylindrical domain (0, T] x G := D rcup Rm+1. The right-hand sides of the system are Volterra type functionals of the unknown function z. In the paper, we give methods of the construction of the monotone iterative sequences converging to the unique classical solution of the problem considered in partially ordered Banach spaces with various convergence rates of iterations. We also give remarks on monotone iterative methods in connection with numerical methods, remarks on methods for the construction of lower and upper solutions and remarks concerning the possibility of extending these methods to more general parabolic equations. All monotone iterative methods are based on differential inequalities and, in this paper, we use the theorem on weak partial differential-functional inequalities for infinite systems of parabolic equations, the comparison theorem and the maximum principle. A part of the paper is based on the results of our previous papers. These results generalize the results obtained by several authors in numerous papers for finite systems of semilinear parabolic differential equations to encompass the case of infinite systems of semilinear parabolic differential-functional equations. The monotone iterative schemes can be used for the computation of numerical solutions.
    Źródło:
    Opuscula Mathematica; 2005, 25, 1; 29-99
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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