On a solvability of a nonlinear fractional reaction-diffusion system in the H\"{o}lder spaces

  • Mykola Krasnoschok Institute of Applied Mathematics and Mechanics of NASU
  • Nataliya V. Vasylyeva Institute of Applied Mathematics and Mechanics of NASU

Abstract

In this paper we analyze  the nonlinear fractional reaction-diffusion (NFRD) system. First, we establish the unique solvability in the H\"{o}lder space of the initial value/ boundary value problem for the fractional diffusion equation $\partial^{\alpha}_{t}u(x,t)=Lu(x,t)+f_{0}(x,t),$ $\alpha\in(0,1),$ where $L$ is a uniformly elliptic operator with smooth coefficients.Second, we apply the contraction theorem to prove the existence and uniqueness in the H\"{o}lder classes of the solution to NFRD system.
Published
2013-11-23
Section
Articles