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Steel and Composite Structures Volume 48, Number 6, September 25 2023 , pages 611-623 DOI: https://doi.org/10.12989/scs.2023.48.6.611 |
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Optimal control formulation in the sense of Caputo derivatives: Solution of hereditary properties of inter and intra cells |
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Muzamal Hussain, Saima Akram, Mohamed A. Khadimallah, Madeeha Tahir, Shabir Ahmad, Mohammed Alsaigh and Abdelouahed Tounsi
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| 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 | ||