TY - JOUR T1 - Semi-Linear Fractional $σ$-Evolution Equations with Nonlinear Memory AU - Kainane Mezadek , Abdelatif JO - Journal of Partial Differential Equations VL - 4 SP - 291 EP - 312 PY - 2020 DA - 2020/08 SN - 33 DO - http://doi.org/10.4208/jpde.v33.n4.1 UR - https://global-sci.org/intro/article_detail/jpde/17861.html KW - Fractional equations, $σ$-evolution equations, global in time existence, small data solutions, nonlinear memory. AB -

In this paper we study the local or global (in time) existence of small data solutions to semi-linear fractional $σ$−evolution equations with nonlinear memory. Our main goal is to explain on the one hand the influence of the memory term and on the other hand the influence of higher regularity of the data on qualitative properties of solutions.