Positive Solutions for Tempered Riemann–Liouville Fractional Equations with Signed Measure and Sign-Changing Perturbations via Spectral Analysis

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.