The necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.
Receipt date:10/27/2021 accepted date:12/15/2021 Publication date:31/12/2021
This work is licensed under a Creative Commons Attribution 4.0 International License.
The phenomenon of extremist extremism (terrorism) was one of the most prominent issues that took a large space in the twenty-first century, in which cognitive motives were mixed with strategic and ideological motives, leading to the emergence of terrorist extremi
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