Fractional order optimal control for biological model

Mohamed Amine Khadimallah, Shabbir Ahmad, Muzamal Hussain and Abdelouahed Tounsi

Abstract

In this research, we considered fractional order optimal control models for cancer, HIV treatment and glucose.These models are based on fractional order differential equations that describe the dynamics underlying the disease.It is formulated in term of left and right Caputo fractional derivative. Pontryagin's Maximum Principle is used as a necessary condition to find the optimal curve for the respective controls over fixed time period. The formulated problems are numerically solved using forward backward sweep method with generalized Euler scheme.

Key Words

Caputo fractional derivative; fractional order differential equations; Pontryagin

Address

Mohamed Amine Khadimallah: Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia Shabbir Ahmad: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan Muzamal Hussain: 1) Department of Mathematics, University of Sahiwal, Sahiwal, Pakistan, 2) Department of Mathematics, University of Sahiwal, Sahiwal, 57000, Punjab, Pakistan Abdelouahed Tounsi: 1) YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea, 2) Department of Civil and Environmental Engineering, King Fahd University of Petroleumand Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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