- Tytuł:
- Diffusion equation including a local fractional derivative and weighted inner product
- Autorzy:
-
Cetinkaya, Suleyman
Demir, Ali - Powiązania:
- https://bibliotekanauki.pl/articles/2175506.pdf
- Data publikacji:
- 2022
- Wydawca:
- Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
- Tematy:
-
local fractional derivative
Dirichlet boundary conditions
spectral method
separation of variables
weighted inner product
lokalna pochodna ułamkowa
warunek brzegowy Dirichleta
metoda spektralna
separacja zmiennych - Opis:
- In this research, we discuss the construction of the analytic solution of the homogenous initial boundary value problem including partial differential equations of fractional order. Since the homogenous initial boundary value problem involves a local fractional order derivative, it has classical initial and boundary conditions. By means of separation of the variables method and the inner product defined on L2 [0, l], the solution is constructed in the form of a Fourier series including the exponential function. The illustrative examples present the applicability and influence of the separation of variables method on time fractional diffusion problems. Moreover, as the fractional order α tends to 1, the solution of the fractional diffusion problem tends to the solution of the diffusion problem which proves the accuracy of the solution.
- Źródło:
-
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 1; 19--27
2299-9965 - Pojawia się w:
- Journal of Applied Mathematics and Computational Mechanics
- Dostawca treści:
- Biblioteka Nauki
Artykuł