Investigating of an immune system-cancer mathematical model with Mittag-Leffler kernel

Necati Özdemir; Esmehan Uçar; Necati Özdemir; Esmehan Uçar

doi:10.3934/math.2020104

AIMS Mathematics

2020, Volume 5, Issue 2: 1519-1531. doi: 10.3934/math.2020104

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Investigating of an immune system-cancer mathematical model with Mittag-Leffler kernel

Necati Özdemir ^,,
Esmehan Uçar

Department of Mathematics, Faculty of Science and Arts, Balıkesir University, Turkey

Received: 29 October 2019 Accepted: 09 January 2020 Published: 21 January 2020
MSC : 34A08, 34A34, 47H10

Cancer that is difficult to treat, is a very common disease today and there are many types of cancer such as lung, colon, stomach. When cancer settles in the body, the immune system tries to resist it. In this study, the mathematical model of the interaction between immune system components and cancer is discussed and is modified by using Atangana-Baleanu derivative. After investigating the existence and uniqueness of the solution of the fractional immune system-cancer model, numerical simulations are given via predictor-corrector scheme.
- immune system-cancer,
- fractional calculus,
- Atangana-Baleanu derivative,
- dendritic cells and IL-2,
- fixed point theory
Citation: Necati Özdemir, Esmehan Uçar. Investigating of an immune system-cancer mathematical model with Mittag-Leffler kernel[J]. AIMS Mathematics, 2020, 5(2): 1519-1531. doi: 10.3934/math.2020104

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Abstract

Cancer that is difficult to treat, is a very common disease today and there are many types of cancer such as lung, colon, stomach. When cancer settles in the body, the immune system tries to resist it. In this study, the mathematical model of the interaction between immune system components and cancer is discussed and is modified by using Atangana-Baleanu derivative. After investigating the existence and uniqueness of the solution of the fractional immune system-cancer model, numerical simulations are given via predictor-corrector scheme.

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