Well-posedness for Cauchy fractional problem involving discrete convolution operators

Abstract

This work is focused in establishing sufficient conditions to guarantee the well-posedness of the following nonlinear fractional semidiscrete modelunder the assumptions that β ∈ (0, 1], c > 0 some constant, B is a discrete convolution operator with kernel b ∈ ℓ 1 (Z), which is the infinitesimal generator of the Markovian C 0 -semigroup and suitable nonlinearity f . We present results concerning the existence and uniqueness of solution, as well as establishing a comparison principle of solutions according to respective initial values and applications.