This work focuses on investigating coupled systems of nonlinear fractional differential equations on the half-axis, involving tempered \(\psi \) -fractional derivatives that multiply the power law kernel by an exponential damping factor. Under much less restrictive conditions than those commonly imposed in the literature, the existence and uniqueness of the solution are proved using Perov’s type fixed point theorem. The continuous dependence of the solution on the initial conditions is also discussed. The key idea in our analysis is the introduction of a generalized locally convex space equipped with a carefully chosen family of vector-valued weighted semi-norms acting on compact subsets of the half-axis.
