Semi-Linear Fractional $σ$-Evolution Equations with Nonlinear Memory (Journal of Partial Differential Equations, 2020)
"In this paper we study the local or global (in time) existence of small data solutions to semi-linear fractional $\u03c3$\u2212evolution 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."
Keywords: Fractional equations; $σ$-evolution equations; global in time existence; small data solutions; nonlinear memory.