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2021 | 153 | 2 | 169-180
Article title

Fractional Integral Approximation and Caputo Derivatives with Modification of Trapezoidal Rule

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Abstracts
EN
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.
Year
Volume
153
Issue
2
Pages
169-180
Physical description
Contributors
  • Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jl. Raya Bandung-Sumedang KM. 21, Jatinangor, Sumedang, West Java 45363, Indonesia
author
  • Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jl. Raya Bandung-Sumedang KM. 21, Jatinangor, Sumedang, West Java 45363, Indonesia
author
  • Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jl. Raya Bandung-Sumedang KM. 21, Jatinangor, Sumedang, West Java 45363, Indonesia
References
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Document Type
article
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Identifiers
YADDA identifier
bwmeta1.element.psjd-c0ce8c99-b399-49b6-af47-70136a26afeb
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