Optimal control formulation in the sense of Caputo derivatives: Solution of hereditary properties of inter and intra cells

Muzamal Hussain , Saima Akram , Mohamed A. Khadimallah , Madeeha Tahir , Shabir Ahmad , Mohammed Alsaigh , Abdelouahed Tounsi

Abstract

This work considered an optimal control formulation in the sense of Caputo derivatives. The optimality of the fractional optimal control problem. The tumor immune interaction in fractional form provides an excellent tool for the description of memory and hereditary properties of inter and intra cells. So the interaction between effector-cells, tumor cells and are modeled by using the definition of Caputo fractional order derivative that provides the system with long-time memory and gives extra degree of freedom. In addiltion, existence and local stability of fixed points are investigated for discrete model. Moreover, in order to achieve more efficient computational results of fractional-order system, a discretization process is performed to obtain its discrete counterpart. Our technique likewise allows the advancement of results, such as return time to baseline that are unrealistic with current model solvers.

Key Words

Caputo derivatives; discretization process; fractional-order system; hereditary properties

Address

Muzamal Hussain — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Saima Akram and Madeeha Tahir — Department of Mathematics, Govt. College Women University Faisalabad, 38000, Faisalabad, Pakistan
Mohamed A. Khadimallah — Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia
Shabir Ahmad — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Mohammed Alsaigh — Faculty of Economics and administration, King Abdulaziz University, Jeddah, Saudi Arabia
Abdelouahed Tounsi — 1)YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea 2)Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals,31261 Dhahran, Eastern Province, Saudi Arabia

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