The Existence of Positive Solutions for a p-Laplacian Tempered Fractional Diffusion Equation Using the Riemann-Stieltjes Integral Boundary Condition

In this paper, we focus on the existence of positive solutions for a class of p-Laplacian tempered fractional diffusion equations involving a lower tempered integral operator and a Riemann-Stieltjes integral boundary condition. By introducing certain new local growth conditions and establishing an a priori estimate for the Green's function, several sufficient conditions on the existence of positive solutions for the equation are derived by using a fixed point theorem. Interesting points are that the tempered fractional diffusion equation contains a lower tempered integral operator and that the boundary condition involves the Riemann-Stieltjes integral, which can be a changing-sign measure.