Classical solutions of time-fractional quasilinear reaction-diffusion systems
DOI:
https://doi.org/10.3842/umzh.v77i2.1147Keywords:
Caputo derivative, Holder spaces, classical solutionAbstract
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.
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