Existence and Stability of solution to a fractional mathematical model of the brain metabolite variations in the circadian rhythm containing Caputo derivative

This study intends to investigate whether a solution to the model of brain metabolite variations in the circadian rhythm exists. The model is a fractional-order important model with regard to applications. The existence of a unique solution to the fractional brain model (FBM) with Caputo derivative is demonstrated, and the general form of the model is provided. A stability analysis is performed on the solution. In four different cases, the numerical solution to FBM is given using the proposed numerical method.