The Eigenvalue Problem of a Singular Tempered Fractional Equation with the Riemann–Stieltjes Integral Boundary Condition

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.