Hyper-chaos control synchronization for a fractional-order Cattaneo-Christov heat flux hybrid model with an optimal control approach

The Cattaneo-Christov heat flux (CCHF) model is a Lorenz-type hyper-chaotic nonlinear physical hybrid model represented as a system of partial differential equations. The truncated Galerkin technique and similarity transformation are used in this study to transmute the governing continuity, energy and momentum equations into non-linear ordinary differential equations based on Fourier modes. Furthermore, the nondimensional features of the heat transfer fluids, along with the thermophysical attributes of the hybrid nanofluids, are considered external stochastic disturbances within the nonlinear complex system. The investigation of the Cattaneo-Christov hybrid model employs a time operator of Caputo-type derivatives. The study explores hyper-chaos, bifurcation, synchronization, and analytical solutions to manage the hyper-chaos within the fractional-order hybrid nonlinear system. This study has been designated as an innovative contribution because it investigates optimal control formulations, stability analysis, and numerical solutions for the fractional-order CCHF hybrid model for the first time. Finally, computational findings show that the proposed control technique is efficient and applicable in stabilizing fractional-order heat flux hybrid systems.