ANALYSIS OF TUMOR-IMMUNE RESPONSE MODEL BY USING CONFORMABLE FRACTIONAL ORDER DERIVATIVE

Ausif Padder; Rimpi Pal; Afroz .; Ayub Khan

doi:10.56827/SEAJMMS.2022.1803.33

Ausif Padder Department of Applied Sciences, University Institute of Engineering and Technology (UIET), Guru Nanak University, Hyderabad - 501506, Telangana, INDIA
Rimpi Pal Department of Mathematics, Gargi College, University of Delhi, New Delhi, INDIA
Afroz . Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, INDIA
Ayub Khan Department of Mathematics, Jamia Millia Islamia, New Delhi, INDIA

DOI: https://doi.org/10.56827/SEAJMMS.2022.1803.33

Abstract

In this research paper, the authors propose a generalized three-dimensional fractional order tumor-immune response model. The generalization of the model is made by introducing interleukin-2 (IL₂) cell population as the third variable in the proposed system. The study of the proposed model is performed by using a new concept of fractional-order derivatives called as conformable fractional-order derivative. The authors aim to study, analyze, and compare the dynamical be- havior of both the three-dimensional fractional order model and the conformable fractional order version of the proposed model. The stability analysis is done for both versions of the model at the biologically feasible equilibrium points. To vali- date the theoretical results numerically, numerical simulation is performed by using a piecewise constant approximation process.