INVESTIGATION OF FRACTIONAL-ORDERED TUMOR-IMMUNE INTERACTION MODEL VIA FRACTIONAL-ORDER DERIVATIVE

Gauhar Ali, Muhammad Marwan, Ubaid Ur Rahman and Manel Hleili
Additional contact information
Gauhar Ali: ��Department of Mathematics, GPG Jahanzeb College Saidu Sharif (Swat), Khyber Pakhtunkhwa, Pakistan
Muhammad Marwan: School of Mathematics and Statistics, Linyi University, Linyi, Shandong 276005, P. R. China
Ubaid Ur Rahman: ��Department of Mathematics, GPG Jahanzeb College Saidu Sharif (Swat), Khyber Pakhtunkhwa, Pakistan
Manel Hleili: ��Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia

FRACTALS (fractals), 2024, vol. 32, issue 06, 1-10

Abstract: Dynamical analysis of system of ordinary differential equations (ODEs) is an interesting topic among researchers and several tools have been discovered since so far to deal with its several other features. There are many built-in functions designed in MATLAB that researchers can use as a tool for the system of ODEs with integer order but in the similar systems have fractional-order derivative is a difficult task. Therefore, the purpose of this work is to use the Caputo fractional-order derivative to qualitatively analyze and then numerically simulate the tumor-immune system interaction model. Moreover, the Schauder fixed point theorem is used to establish the condition for the existence of at least one solution, while the Banach fixed point theorem is utilized to guarantee the existence of a unique solution. Moreover, the stability in the trajectories of considered system achieved with the aid of Ulam–Hyers (UH) stability. In addition, the numerical computations are performed using Variational Iteration Method (VIM) and the visualized results are shown using MATLAB.

Keywords: Fractional-Ordered Dynamical Systems; Caputo Derivative; Tumor-Immune Interaction; Fixed Point Theory (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X24501196
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:32:y:2024:i:06:n:s0218348x24501196

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X24501196

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().