Fractional Differential Equation as a Models of Newton Fluids for Stress and Strain Problems

DOI

10.2991/icomse-17.2018.43How to use a DOI?

Keywords

Fractional Differential equations, Mittag-Lefler, stress, Strain

Abstract

An ordinary differential equation is a branch of mathematics that is always interesting to be learned and developed due to its numerous variations in both the theory and its application. In general, the most discussed differential equation is the ordinary differential equation that has the natural number as its order. However, currently, the order of a differential equation which has been developed into a fractional-order (i.e. rational numbers) is also very interesting to be studied. This paper presents a study of ordinary differential equations that has fractional order, in which the left side contains two derivative functions with fractional order while the right side contains polynomial function n degree. Specifically, this paper presents the general form of equations, methods of finding the solution in three cases, and its application. Solutions are proposed using the Laplace transformation and its inverse and are expressed in the form of Mittag-Lefler function. Its graph is also later described using Matlab. Results of this research are expressed by three functions of three different theoretical cases and a solution to an application problem. Additionally, the study has also shown that the convergence of a number sequence of fractional differential equation order is positively related to the convergence of solution function sequence. There are many applications of fractional differential equations in the field of viscoelasticity. Therefore, at the end of the paper, this application is presented particularly regarding the relationship between stress and strain for solids and for Newtonian fluids.

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  - Endang Rusyaman
AU  - D Chaerani
AU  - Kankan Parmikanti
PY  - 2017/08
DA  - 2017/08
TI  - Fractional Differential Equation as a Models of Newton Fluids for Stress and Strain Problems
BT  - Proceedings of the 1st Annual International Conference on Mathematics, Science, and Education (ICoMSE 2017)
PB  - Atlantis Press
SP  - 80
EP  - 85
SN  - 2352-5398
UR  - https://doi.org/10.2991/icomse-17.2018.43
DO  - 10.2991/icomse-17.2018.43
ID  - Rusyaman2017/08
ER  -