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Wyszukujesz frazę "równanie Laplace’a" wg kryterium: Temat

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    Wyświetlanie 1-8 z 8
    Tytuł:
    Influence of heat sources and relaxation time on temperature distribution in tissues
    Autorzy:
    Sharma, S.
    Sharma, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/955132.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    wahania temperatury w tkankach
    ciepło biologiczne
    równanie Laplace'a
    źródło ciepła
    Penne's bio-heat equation
    relaxation time
    heat source
    Laplace transform
    Hankel transform
    Opis:
    In the present study, the temperature fluctuations in tissues based on Penne’s bio-heat transfer equation is investigated by applying the Laplace and Hankel transforms. To get the solution in a physical form, a numerical inversion technique has been applied. The temporal and spatial distribution of temperature is investigated with the effect of relaxation time and is presented graphically.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2014, 19, 2; 427-433
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solutions to Time-Fractional Diffusion-Wave Equation in Spherical Coordinates
    Autorzy:
    Povstenko, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/386572.pdf
    Data publikacji:
    2011
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    transformata Laplace'a
    transformata Fouriera
    równanie dyfuzji
    Laplace transform
    Fourier transform
    diffusion equation
    Opis:
    Solutions to time-fractional diffusion-wave equation with a source term in spherical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time t, the finite Fourier transform with respect to the angular coordinate , the Legendre transform with respect to the spatial coordinate , and the Hankel transform of the order n+1/2 with respect to the radial coordinate . In the central symmetric case with one spatial coordinate the obtained results coincide with those studied earlier.
    Źródło:
    Acta Mechanica et Automatica; 2011, 5, 2; 108-111
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator
    Autorzy:
    Kumar, Prem
    Qureshi, Sania
    Powiązania:
    https://bibliotekanauki.pl/articles/122736.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    ordinary differential equations
    Laplace transform
    Riemann-Liouville integral
    równanie różniczkowe zwyczajne
    transformacja Laplace'a
    całka Riemann-Liouville
    Opis:
    Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 57-66
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Using Shehu integral transform to solve fractional order Caputo type initial value problems
    Autorzy:
    Qureshi, Sania
    Kumar, Prem
    Powiązania:
    https://bibliotekanauki.pl/articles/122809.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    ordinary differential equations
    Laplace transform
    Riemann-Liouville integral
    równanie różniczkowe zwyczajne
    transformata Laplace'a
    całka Riemann-Liouville
    Opis:
    In the present research analysis, linear fractional order ordinary differential equations with some defined condition (s) have been solved under the Caputo differential operator having order α > 0 via the Shehu integral transform technique. In this regard, we have presented the proof of finding the Shehu transform for a classical nth order integral of a piecewise continuous with an exponential nt h order function which leads towards devising a theorem to yield exact analytical solutions of the problems under investigation. Varying fractional types of problems are solved whose exact solutions can be compared with solutions obtained through existing transformation techniques including Laplace and Natural transforms.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 75-83
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator
    Autorzy:
    Kumar, Prem
    Qureshi, Sania
    Powiązania:
    https://bibliotekanauki.pl/articles/1839810.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    ordinary differential equations
    Laplace transform
    Riemann-Liouville integral
    równanie różniczkowe zwyczajne
    transformacja Laplace'a
    całka Riemann-Liouville
    Opis:
    Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 57-66
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Eigen value approach to generalized thermoelastic interactions in an unbounded body with circular cylindrical cavity without energy dissipation
    Autorzy:
    Chakraborty, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/264348.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    eigen value approach
    generalized thermoelasticity
    Laplace transform
    vector-matrix differential equation
    termoelastyczność
    transformata Laplace'a
    równanie różniczkowe
    macierze
    Opis:
    The theory of generalized thermoelasticity in the context of the Green-Naghdi model -II (thermoelasticity without energy dissipation) is studied for an infinite circular cylindrical cavity subjected to two different cases of thermoelastic interactions when the radial stress is zero for (a) maintaining constant temperature and (b) temperature is varying exponentially with time. The Laplace transform from time variable is used to the governing equations to formulate a vector matrix differential equation which is then solved by the eigen value approach. Numerical computations for the displacement component, temperature distribution and components of thermal stress have been made and presented graphically.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2017, 22, 4; 811-825
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fourier, Laguerre, Laplace Transforms with applications
    Autorzy:
    Aghili, Arman
    Powiązania:
    https://bibliotekanauki.pl/articles/2052384.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    Fourier transform
    Laplace transform
    Laguerre transform
    singular integral equation
    Bessel's functions
    fractional heat equation
    przekształcenie Fouriera
    przekształcenie Laplace'a
    przekształcenie Laguerre'a
    osobliwe równanie całkowe
    funkcje Bessela
    ułamkowe równanie ciepła
    Opis:
    In this article, the author considered certain time fractional equations using joint integral transforms. Transform method is a powerful tool for solving singular integral equations, integral equation with retarded argument, evaluation of certain integrals and solution of partial fractional differential equations. The obtained results reveal that the transform method is very convenient and effective. Illustrative examples are also provided.
    Źródło:
    Journal of Mathematics and Applications; 2021, 44; 5-17
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of solutions of the 1D fractional Cattaneo heat transfer equation
    Autorzy:
    Siedlecka, Urszula
    Ciesielski, Mariusz
    Powiązania:
    https://bibliotekanauki.pl/articles/2175501.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    heat transfer
    Cattaneo equation
    fractional Caputo derivative
    Laplace transform
    Fourier transform
    wymiana ciepła
    równanie Cattaneo
    pochodna ułamkowa Caputo
    transformata Laplace'a
    transformata Fouriera
    Opis:
    In this paper, a solution of the single-phase lag heat conduction problem is presented. The research concerns the generalized 1D Cattaneo equation in a whole-space domain, where a second order time derivative is replaced by the fractional Caputo derivative. The Fourier-Laplace transform technique is used to determine a solution of the considered problem. The numerical inversion of the Laplace transforms is applied. The effect of the order of the fractional derivative on the temperature distribution is investigated.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 4; 87--98
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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