- Tytuł:
- Fractional Integral Approximation and Caputo Derivatives with Modification of Trapezoidal Rule
- Autorzy:
-
Pandiangan, Naomi
Johar, Dwindi
Purwani, Sri - Powiązania:
- https://bibliotekanauki.pl/articles/1193326.pdf
- Data publikacji:
- 2021
- Wydawca:
- Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
- Tematy:
-
Caputo fractional derivative
Fractional integral
Modified trapezoidal rule
Rieman Liouville fractional integral - Opis:
- In classical calculus, a function can be derived or integrated as many as natural numbers. Then a question arises regarding the fractional order of derivatives and integrals. There is a development of classical calculus called fractional calculus. Fractional calculus may be a department of science that amplifies the orders of derivatives and integrals into the order of rational numbers or even real numbers. The difficulty of finding solutions analytically for a complicated function of fractional integrals or fractional derivatives often occurs. In this paper, we will solve Rieman Liouville's fractional integral and Caputo's fractional derivative analytically using the trapezoidal rule modification method. Trapezoidal method is an approximation method that is resulted from the linear interpolation function. In this paper, we will find numerical simulations with modified trapezoidal method, to estimate some functions, and the results will be compared with previous research related to the Rieman Liouville fractional integral approximation and the Caputo fractional derivative. The result from simulation find that modified trapezoidal can approximate Caputo fractional derivative by replace α with -α and Quadratic schemes method is the best method to approximate Rieman Liouville fractional integral and Caputo fractional derivative.
- Źródło:
-
World Scientific News; 2021, 153, 2; 169-180
2392-2192 - Pojawia się w:
- World Scientific News
- Dostawca treści:
- Biblioteka Nauki
Artykuł