Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 290
Non-linear age dependent population dynamics with a fractional time derivative
Hiba El Asraoui, Khalid Hilal, Abdelmajid El Hajaji
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 29, 2022
March 03, 2252
April 15, 2252

Abstract: The model introduced by Gurtin and MacCamy in [1] to describe the dynamics of populations, is one of the most widely studied problems (see for example [3], [4]). In the present work we reconsidered this model with a fractional time derivative. Using the fractional Lagrange characteristic method, given by Jumarie Guy in [2], we showed that the given population problem is equivalent to a pair of integral equations where the unknown functions are the total population P(t), and the birth rate B(t). We used these equations to prove that the solution exists and is unique in a sufficiently small ...