Optimal control for cancer treatment mathematical model using Atangana-Baleanu-Caputo fractional derivative

被引：56

作者：

Sweilam, Nasser Hassan ^{[1
]}

Al-Mekhlafi, Seham Mahyoub ^{[2
]}

Assiri, Taghreed ^{[3
]}

Atangana, Abdon ^{[4
]}

机构：

[1] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt

[2] Sanaa Univ, Fac Educ, Dept Math, Sanaa, Yemen

[3] Umm Alqura Univ, Fac Sci, Dept Math, Mecca, Saudi Arabia

[4] Univ Free State, Fac Nat & Agr Sci, Inst Groundwater Studies, ZA-9300 Bloemfontein, South Africa

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

Fractional-order derivatives; Mathematical cancer models; Anti-angiogenic therapy; Immunotherapy; Iterative optimal control method; The nonstandard two-step Lagrange interpolation method; 37N25; 49J15; 26A33; FINITE-DIFFERENCE SCHEMES; TUMOR; EQUATIONS; GROWTH; FORMULATION; TRENDS; IMPACT;

D O I：

10.1186/s13662-020-02793-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, optimal control for a fractional-order nonlinear mathematical model of cancer treatment is presented. The suggested model is determined by a system of eighteen fractional differential equations. The fractional derivative is defined in the Atangana-Baleanu Caputo sense. Necessary conditions for the control problem are derived. Two control variables are suggested to minimize the number of cancer cells. Two numerical methods are used for simulating the proposed optimal system. The methods are the iterative optimal control method and the nonstandard two-step Lagrange interpolation method. In order to validate the theoretical results, numerical simulations and comparative studies are given.

引用

页数：21

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