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

Lishuang Li, Xinguang Zhang (), Peng Chen and Yonghong Wu
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Lishuang Li: School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, China
Xinguang Zhang: School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, China
Peng Chen: School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, China
Yonghong Wu: Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia

Mathematics, 2025, vol. 13, issue 3, 1-16

Abstract: 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.

Keywords: tempered fractional equations; Riemann–Stieltjes integral; fixed point theorem; positive solutions; p-Laplacian operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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