In this paper, we investigate the existence of positive solutions for a class of p-Laplacian tempered Riemann–Liouville fractional equations involving signed measures and sign-changing perturbations with Riemann–Stieltjes boundary conditions. By performing a spectral analysis of the associated linear operator and applying Gelfand’s formula, we establish several fundamental properties of the principal eigenvalue for the corresponding linear fractional-order differential equations. Furthermore, under suitable growth conditions on the nonlinear terms, we employ the fixed point index theory to derive new existence results for positive solutions of the proposed equations.

In this paper, we investigate the existence of positive solutions of the eigenvalue problem for a singular tempered fractional equation with a Riemann–Stieltjes integral boundary condition and signed measures. By establishing the Green function and its properties, an eigenvalue interval for the existence of positive solutions is outlined based on Schauder’s fixed-point theorem and the upper and lower solutions method. An interesting feature of this paper is that f may be singular in both the time and space variables, and the Riemann–Stieltjes integral may involve signed measures.