A Comparative Teaching of Fractional Calculus and Integer Calculus

DOI

10.2991/icsser-18.2018.22How to use a DOI?

Keywords

Fractional calculus; Integral order calculus; Riemann-Liouville derivative; Riemann-Liouville integral; Comparative teaching

Abstract

The main purpose of this paper is to give a teaching comparison of fractional calculus and integer calculus. Another purpose of this paper is to help students to understand fractional calculus and integer calculus are highly unified. Starting from the integral order derivative of the elementary power function, the definition of Riemann-Liouville fractional derivative is given. With the theory of integral calculus such as integral mean value theory, Green formula and classical inequality, the fractional differential equations are transformed into integers order differential equation, the differences and relations between two kinds of calculus are expounded. Therefore, it is concluded that fractional derivative and integral derivative can be exchanged under certain conditions.

Copyright

© 2018, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Qingxia Ma
AU  - Xianguang Lin
AU  - Huijuan Li
PY  - 2018/10
DA  - 2018/10
TI  - A Comparative Teaching of Fractional Calculus and Integer Calculus
BT  - Proceedings of the 2018 International Conference on Social Science and Education Reform (ICSSER 2018)
PB  - Atlantis Press
SP  - 94
EP  - 97
SN  - 2352-5398
UR  - https://doi.org/10.2991/icsser-18.2018.22
DO  - 10.2991/icsser-18.2018.22
ID  - Ma2018/10
ER  -