Classical solutions of time-fractional quasilinear reaction-diffusion systems

UDC 517.9 We analyze a quasilinear reaction-diffusion system with the time-fractional Caputo derivative. We prove the existence and uniqueness result to initial-boundary problems with Dirichlet and Robin (Neumann) boundary conditions under suitable assumptions on the given data. The existence of the solution to our problem is proved by the Leray–Schauder fixed-point theorem. Positivity property allows us to apply the method of upper-lower solutions. We provide an example of upper and lower solutions to some specific time-fractional reaction-diffusion system.