Modeling Alcohol Concentration in Blood via a Fractional Context

• Main Authors: Omar Rosario Cayetano, Alberto Fleitas Imbert, José Francisco Gómez-Aguilar, Antonio Fernando Sarmiento Galán
• Format: Article
• Language: English
• Published: MDPI AG 2020-03-01
• Series: Symmetry
• Subjects: fractional calculus; conformable and non-conformable derivatives; bayesian estimation
• Online Access: https://www.mdpi.com/2073-8994/12/3/459

We use a conformable fractional derivative <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>G</mi> <mrow> <mi>T</mi> </mrow> <mi>&#945;</mi> </msubsup> </semantics> </math> </inline-formula> through two kernels <inline-formula> <math display="inline"> <semantics> <mrow> <mi>T</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>&#945;</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mi>e</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>&#945;</mi> <mo>&#8722;</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mi>t</mi> </mrow> </msup> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>T</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>&#945;</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mi>t</mi> </mrow> <mrow> <mn>1</mn> <mo>&#8722;</mo> <mi>&#945;</mi> </mrow> </msup> </mrow> </semantics> </math> </inline-formula> in order to model the alcohol concentration in blood; we also work with the conformable Gaussian differential equation (CGDE) of this model, to evaluate how the curve associated with such a system adjusts to the data corresponding to the blood alcohol concentration. As a practical application, using the symmetry of the solution associated with the CGDE, we show the advantage of our conformable approaches with respect to the usual ordinary derivative.