### Journals Information

**
Mathematics and Statistics Vol. 10(1), pp. 134 - 139 DOI: 10.13189/ms.2022.100110 Reprint (PDF) (252Kb) **

## Viscosity Analysis of Lubricating Oil Through the Solution of Exponential Fractional Differential Equations

**Endang Rusyaman ^{1}^{,*}, Kankan Parmikanti ^{1}, Diah Chaerani ^{1}, Khoirunnisa Rohadatul Aisy Muslihin ^{2}**

^{1}Department of Mathematics, FMIPA, Universitas Padjadjaran, Indonesia

^{2}Universitas Padjadjaran, Indonesia

**ABSTRACT**

Lubricating oil is still a primary need for people dealing with machines. The important thing of lubricating oil is viscosity which is closely related to surface tension. Fluid viscosity states the measure of friction in the fluid, while surface tension is the tendency of the fluid to stretch due to attractive forces between the molecules (cohesion). We want to know how and to what extent the relationship between viscosity and surface tension of the lubricating oil is. This paper will discuss the analysis of a model in the form of an exponential fractional differential equation that states the relationship between surface tension and viscosity of lubricating oil. The Modified Homotopy Perturbation Method (MHPM) will be used to determine the solution of the fractional differential equation. This study indicates a relationship between viscosity and surface tension in the form of fractional differential equation in which the existence and uniqueness of the solution are guaranteed. From the analysis of the solution function both analytically and geometrically supported by empirical data, it can be concluded that there is a strong exponential relationship between viscosity and surface tension in lubricating oil.

**KEYWORDS**

Exponential, Fractional Differential Equation, Surface Tension, Viscosity

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Endang Rusyaman , Kankan Parmikanti , Diah Chaerani , Khoirunnisa Rohadatul Aisy Muslihin , "Viscosity Analysis of Lubricating Oil Through the Solution of Exponential Fractional Differential Equations," Mathematics and Statistics, Vol. 10, No. 1, pp. 134 - 139, 2022. DOI: 10.13189/ms.2022.100110.

(b). APA Format:

Endang Rusyaman , Kankan Parmikanti , Diah Chaerani , Khoirunnisa Rohadatul Aisy Muslihin (2022). Viscosity Analysis of Lubricating Oil Through the Solution of Exponential Fractional Differential Equations. Mathematics and Statistics, 10(1), 134 - 139. DOI: 10.13189/ms.2022.100110.