Wszystkie pola: initial value problems - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

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Skocz do pozycji: 2.

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

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Skocz do pozycji: 3.

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

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Skocz do pozycji: 4.

Tytuł:: A new numerical technique for solving fractional Bratu’s initial value problems in the Caputo and Caputo-Fabrizio sense
Autorzy:: Khalouta, Ali
Kadem, Abdelouahab
Powiązania:: https://bibliotekanauki.pl/articles/1839797.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: fractional Bratu’s initial value problem
Caputo fractional derivative
Caputo-Fabrizio fractional derivative
natural transform method
Adomian decomposition method
ułamkowa pochodna Caputo
ułamkowa pochodna Caputo-Fabrizio
metoda transformacji naturalnej
metoda dekompozycji Adomiana
Opis:: The purpose of this paper is to propose a new numerical technique called the natural decomposition method (NDM) for solving fractional Bratu’s initial value problems (FBIVP) in the Caputo and Caputo-Fabrizio sense. The NDM is a combined form of the natural transform method and the Adomian decomposition method. The numerical example is provided in order to validate the efficiency and reliability of the proposed method. The obtained results reveal that the proposed method is a very efficient and simple tool for solving fractional differential equations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 43-56
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: A new numerical technique for solving fractional Bratu’s initial value problems in the Caputo and Caputo-Fabrizio sense
Autorzy:: Khalouta, Ali
Kadem, Abdelouahab
Powiązania:: https://bibliotekanauki.pl/articles/122619.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: fractional Bratu’s initial value problem
Caputo fractional derivative
Caputo-Fabrizio fractional derivative
natural transform method
Adomian decomposition method
ułamkowa pochodna Caputo
ułamkowa pochodna Caputo-Fabrizio
metoda transformacji naturalnej
metoda dekompozycji Adomiana
Opis:: The purpose of this paper is to propose a new numerical technique called the natural decomposition method (NDM) for solving fractional Bratu’s initial value problems (FBIVP) in the Caputo and Caputo-Fabrizio sense. The NDM is a combined form of the natural transform method and the Adomian decomposition method. The numerical example is provided in order to validate the efficiency and reliability of the proposed method. The obtained results reveal that the proposed method is a very efficient and simple tool for solving fractional differential equations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 43-56
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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