Comparison of the Trapezoidal Rule and Simpson's Rule in the Riemann-Liouville Fractional Integral Approach

Khoirunnisa Rohadatul Aisy Muslihin; Wida Nurul Fauziyah; Sri Purwani

doi:10.47194/orics.v3i4.200

Authors

Khoirunnisa Rohadatul Aisy Muslihin
khoirunnisa17002@mail.unpad.ac.id
Master's Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor, Indonesia
Wida Nurul Fauziyah Master's Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor, Indonesia
Sri Purwani Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor, Indonesia

Keywords:

Fractional calculus, Riemann-Liouville fractional integral, trapezoidal rule, Simpsonâ€™s rule

Abstract

Research on calculus has developed a lot, including fractional calculus. Fractional calculus is a branch of mathematics that transforms the orders of derivatives and integrals into rational or even real values. In finding the value of the derivative and the fractional integral, a numerical method is needed to find it, because of the difficulty if it is done using an analytical method. In this paper, we will describe the Riemann-Liouville fractional integral approach using the trapezoidal rule and Simpson's rule. We also provide an overview of the comparisons and errors that result from the two methods.Â

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