Open AccessDynamical behavior of tumor-immune system with fractal-fractional operator
Author(s) -
Muhammad Farman,
Aqeel Ahmad,
Ali Akgül,
Muhammad Umer Saleem,
Kottakkaran Sooppy Nisar,
V. Vijayakumar
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022489
Subject(s) - fractional calculus , fractal , nonlinear system , mathematics , operator (biology) , discretization , stability (learning theory) , mathematical analysis , physics , computer science , quantum mechanics , biochemistry , chemistry , repressor , machine learning , transcription factor , gene
In this paper, the dynamical behavior of the fractional-order cancer model has been analyzed with the fractal-fractional operator, which discretized the conformable cancer model. The fractional-order model consists of the system of nonlinear fractional differential equations. Also, we discuss the fractional-order model to check the relationship between the immune system and cancer cells by mixing IL-12 cytokine and anti-PD-L1 inhibitor. The tumor-immune model has been studied qualitatively as well as quantitatively via Atangana-Baleanu fractal-fractional operator. The nonlinear analysis is used to check the Ulam-Hyres stability of the proposed model. Moreover, the dynamical behavior for the fractional-order model has been checked by using a fractal-fractional operator with a generalized Mittag-Leffler Kernel and verifying the effect of fractional parameters. Finally, the obtained solutions are interpreted biologically, and simulations are carried out to illustrate cancer disease and support theoretical results, which will be helpful for further analysis and to control the effect of cancer in the community.