### Journals Information

**
Mathematics and Statistics Vol. 10(6), pp. 1194 - 1205 DOI: 10.13189/ms.2022.100605 Reprint (PDF) (438Kb) **

## Modified Mathematical Models in Biology by the Means of Caputo Derivative of a Function with Respect to Another Exponential Function

**Jamal Salah ^{1}^{,*}, Maryam Al Hashmi ^{1}, Hameed Ur Rehman ^{2}, Khaled Al Mashrafi ^{1}**

^{1}Department of Basic Science, College of Applied and Health Science, A’Sharqiyah University, Post Code 42, 400 Ibra, Oman

^{2}Department of Mathematics, Center for Language and Foundation Studies, A’Sharqiyah University, Post Code 42, 400 Ibra, Oman

**ABSTRACT**

In this article, the researcher considered some well-known mathematical models of ordinary differential equations applied in biology such as the bacterial growth, the natural FC solution models for vegetables, the biological phospholipids pathway, the glucose absorption by the body and the spread of epidemics. The ordinary differential equations for each model are fractionalized by the means of Caputo derivative of a function with respect to certain exponential function. In each model, we embed the concept fractionalization associated with a chosen exponential function in order to modify the given model. Consequently, various propositions are evoked by hypothetically allowing some modifications in several mathematical models of biology. The results are further visualized by providing the graphs of Mittag-Leffler function on various parameters. The graphs' analysis explored the behavior of the solution for every modified model. In this study, the solutions of the modified models are all of the Mittag–Leffler form while all original models are solved by the means of exponential function. Slight changes of the behavior of the solutions are due to the assumptions and the change of parameters.

**KEYWORDS**

Fractional Calculus, Mittag-Leffler Function, Monod Equation, Caputo-type Derivatives

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

(a). IEEE Format:

[1] Jamal Salah , Maryam Al Hashmi , Hameed Ur Rehman , Khaled Al Mashrafi , "Modified Mathematical Models in Biology by the Means of Caputo Derivative of a Function with Respect to Another Exponential Function," Mathematics and Statistics, Vol. 10, No. 6, pp. 1194 - 1205, 2022. DOI: 10.13189/ms.2022.100605.

(b). APA Format:

Jamal Salah , Maryam Al Hashmi , Hameed Ur Rehman , Khaled Al Mashrafi (2022). Modified Mathematical Models in Biology by the Means of Caputo Derivative of a Function with Respect to Another Exponential Function. Mathematics and Statistics, 10(6), 1194 - 1205. DOI: 10.13189/ms.2022.100605.