Chaos in Cancer Tumor Growth Model with Commensurate and Incommensurate Fractional-Order Derivatives

Nadjette Debbouche; Adel Ouannas; Giuseppe Grassi; Abdul-Basset A Al-Hussein; Fadhil Rahma Tahir; Khaled M Saad; Hadi Jahanshahi; Ayman A Aly

doi:10.1155/2022/5227503

Chaos in Cancer Tumor Growth Model with Commensurate and Incommensurate Fractional-Order Derivatives

Comput Math Methods Med. 2022 May 20:2022:5227503. doi: 10.1155/2022/5227503. eCollection 2022.

Authors

Nadjette Debbouche¹, Adel Ouannas¹, Giuseppe Grassi², Abdul-Basset A Al-Hussein³, Fadhil Rahma Tahir³, Khaled M Saad⁴, Hadi Jahanshahi⁵, Ayman A Aly⁶

Affiliations

¹ Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria.
² Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy.
³ Electrical Engineering Department, College of Engineering, University of Basrah, Basrah, Iraq.
⁴ Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen.
⁵ Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada.
⁶ Department of Mechanical Engineering, College of Engineering, Taif University, P.O.Box 11099, Taif 21944, Saudi Arabia.

Abstract

Analyzing the dynamics of tumor-immune systems can play an important role in the fight against cancer, since it can foster the development of more effective medical treatments. This paper was aimed at making a contribution to the study of tumor-immune dynamics by presenting a new model of cancer growth based on fractional-order differential equations. By investigating the system dynamics, the manuscript highlights the chaotic behaviors of the proposed cancer model for both the commensurate and the incommensurate cases. Bifurcation diagrams, the Lyapunov exponents, and phase plots confirm the effectiveness of the conceived approach. Finally, some considerations regarding the biological meaning of the obtained results are reported through the manuscript.

MeSH terms

Humans
Models, Statistical*
Neoplasms*
Nonlinear Dynamics*