Numerical analysis of fractional human liver model in fuzzy environment

Abstract

Many papers have shown that fractional derivatives are preferable to other operators when the data or information is exact, but this is not the case in practice because we live in an uncertain environment. Fuzzy operators are the best option for modelling in this situation. In this paper, we use the fuzzy fractional Caputo's derivative to generalize the fractional-order human liver model. We consider both types of H-differentiability (type 1 and type 2). We establish a general procedure of solution under the concept of H-differentiability through fuzzy Laplace transform. We implement the proposed scheme to derive the numerical results of the model. We present the archived theoretical solution via two- and three-dimensional graphs at different values of fractional orders and specific fuzzy triangular initial conditions. We present the evolution of the proposed model for some values of $ \varphi _0\in [0,1] $ to see the effect of uncertainty on the secretion of Bromsulphthalein in the blood and liver.

Keywords

• human liver model
• fuzzy fractional derivative
• uncertainty
• fuzzy laplace transform
• h-differentiability