The Necessary and Sufficient Optimality Conditions for a System of FOCPs with Caputo–Katugampola Derivatives


  • Moataz Abbas Holel Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq. Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq.
  • Sameer Qasim Hasan Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq.



Calculus of variations, Caputo–Katugampola fractional derivative, Hamiltonian system, Necessary and sufficient optimality conditions, Optimal control


The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of CaputoKatugampola 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 CaputoKatugampola 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.


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