Fractional optimal control problems on a star graph: Optimality system and numerical solution

In this paper, we study optimal control problems for nonlinear fractional order boundary value on a star graph, where the derivative is described in Caputo sense. The adjoint state and optimality system are derived problem (FOCP) by using Lagrange multiplier method. Then, existence uniqueness of solution equation proved means Banach contraction principle. We also present numerical method to find approximate resulting system. In proposed method, \begin{document}$ L2 $\end{document} scheme Grünwald-Letnikov formula used approximation right Riemann-Liouville derivative, respectively, which converts into linear algebraic equations. Two examples provided demonstrate feasibility