Abstract

This work focused on establishing sufficient conditions to guarantee the well-posedness of the following nonlinear fractional semidiscrete model: {Dtβu(n,t)=Bu(n,t)+f(n-ct,u(n,t)),n∈Z,t>0,u(n,0)=φ(n),n∈Z, under the assumptions that β∈ (0 , 1] , c> 0 some constant, and B is a discrete convolution operator with kernel b∈ ℓ1(Z) , which is the infinitesimal generator of the Markovian C -semigroup and suitable nonlinearity f. We present results concerning the existence and uniqueness of solutions, as well as establishing a comparison principle of solutions according to the respective initial values.