Weakly Coupled System of Semi-Linear Fractional θ-Evolution Equations with Special Cauchy Conditions

Abstract

In this paper, we consider a weakly system of fractional θ-evolution equations. Using the fixed-point theorem, a global-in-time existence of small data solutions to the Cauchy problem is proved for one single equation. Using these results, we prove the global existence for the system under some mixed symmetrical conditions that describe the interaction between the equations of the system.