Research Article AFractionalEpidemiologicalModelforBoneRemodelingProcess Muath Awadalla , 1 Yves Yannick Yameni Noupoue , 2 and Kinda Abuasbeh 1 1 Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia 2 Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA), Universite Catholique de Louvain (UCLouvain), Louvain-la-Neuve 1348, Belgium Correspondence should be addressed to Kinda Abuasbeh; kabuasbeh@kfu.edu.sa Received 10 May 2021; Revised 14 September 2021; Accepted 22 October 2021; Published 10 November 2021 Academic Editor: Jos´ e Francisco G´ omez Aguilar Copyright © 2021 Muath Awadalla et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is article focuses on modeling bone formation process using a fractional differential approach, named bones remodeling process. e first goal of the work is to investigate existence and uniqueness of the proposed fractional differential model. e next goal is to investigate how similar is the proposed approach to the method based on system classical differential equations. e dynamical system of equations used is built upon three main parameters. ese are chemical substances, namely, calcitonin secretion, osteoclastic and osteoblastic, which are involved in the bone’s formation process. We implement some numerical simulations to graphically show the impact of an arbitrary fractional order of derivative. We finally obtained that modeling bone formation process using fractional differential equations yielded comparable results with those obtained through a system of classical differential equations. Flexibility in the choice of the fractional order of derivative is an advantage as it helps in selecting the best fractional order of derivative. 1. Introduction Modeling natural phenomena through differential equation has long been used by scientists. In the early days, differential equations with integer order of derivative were commonly used. en several fractional order derivatives have been implemented. In earlier days of fractional differential equations, researchers mainly focused on theoretical concepts, investigating existence and uniqueness of so- lution of built models. A sample of such theoretical works is found in [1–5]. In general, researchers build models based on fractional differential by analogy to the approach that would be used in the case of classical differential [6–8]. Hence, in many cases, authors will try to compare models’ performances from both approaches. Despite analogies that might exist between classical and fractional models upon a given problem, both models might not have common properties. For instance, the Carleman embedding technique [9] applicable in the studies of classical differential equations does not hold for the fractional differential equations for instance. Beside theoretical study of fractional differential equations, a lot have been done by researchers concerning possible application to real life phenomena. One can mention a nonexhaustive field of study with examples for which fractional differential has been successfully per- formed. In biology, modeling dynamics in human tissues was proposed in [10]. Alcohol can be dangerous when its concentration in high human blood exceeds a certain threshold. In [11], a fractional-based model of alcohol level in blood was proposed. Following the aims to prove the use of fractional dif- ferential equations, we decided to investigate how efficient it will be in modeling bone formation process. Before going into details, we will provide an overview of human bone formation process. Human bone formation and develop- ment are a complex process that starts from when a fetus is 3 months old and ends during teenage years, 13–18 years old. However, bone formation never ends in practice. Indeed, bones are living tissue made up of protein, calcium, and other minerals, as well as water. In this regard, bones’ tissue constantly renews itself, by breaking down older tissue and replacing it with new tissue. is process is called “bone Hindawi Journal of Mathematics Volume 2021, Article ID 1614774, 11 pages https://doi.org/10.1155/2021/1614774