Variational approach to optimal control constrained by fractal-fractional differential equations

The extant corpus of literature pertaining to optimal control problems with partial differential equation (PDE) constraints is extensive. This paper introduces a novel variational approach to optimal control problems constrained by fractal-fractional differential equations. Utilizing the shallow water wave as a case study, the semi-inverse method is employed to establish the variational formulation. This approach not only exemplifies a novel mode of thinking but also has significant ramifications for the field. This novel approach to optimal control paves a promising path for further research and provides researchers and practitioners with a novel perspective and potential avenues for further exploration. By exploring this alternative approach, researchers and practitioners can develop a more profound understanding of the fundamental nature of optimal control problems and identify more effective solutions for a wide range of applications.