New aspects of poor nutrition in the life cycle within the fractional calculus

Dumitru Baleanu,Amin Jajarmi,Mojtaba Hajipour,Ebenezer Bonyah

doi:10.1186/s13662-018-1684-x

Abstract

The nutrition of pregnant women is crucial for giving birth to a healthy baby and even for the health status of a nursing mother. In this paper, the poor nutrition in the life cycle of humans is explored in the fractional sense. The proposed model is examined via the Caputo fractional operator and a new one with Mittag–Leffler (ML) nonsingular kernel. The stability analysis as well as the existence and uniqueness of the solution are investigated, and an efficient numerical scheme is also designed for the approximate solution. Comparative numerical analysis of these two operators reveals that the model based on the new fractional derivative with ML kernel has a different asymptotic behavior to the classic Caputo. Thus, the new aspects of fractional calculus provide more flexible models which help us to adjust the dynamical behaviors of the real-world phenomena better.

Highlights

Nutrition has been a major factor in every human stage of development from conception to old age
The fractional calculus (FC) has a special characteristic of capturing memory effects, which is found in almost all biological systems
We considered a fractional model of pregnant females by using the ABC fractional operator

Summary

Introduction

Nutrition has been a major factor in every human stage of development from conception to old age. Inspired by the above discussions, this paper aims to develop a new fractional mathematical model to investigate new aspects of the poor nutrient status of pregnant women. In this formulation, we use the new definition of FDs with ML nonsingular kernel [35]. Numerical simulations verify that there exists a new asymptotic behavior within this new formulation, which is different from that exhibited by using the other FC derivatives This new model has the potential to better represent hidden aspects of the poor nutrition system in the life cycle than the classic type of fractional operators.

Numerical method

Conclusion