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

Author

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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
    Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia)

  • 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)

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.

Suggested Citation

  • Lishuang Li & Xinguang Zhang & Peng Chen & Yonghong Wu, 2025. "The Existence of Positive Solutions for a p -Laplacian Tempered Fractional Diffusion Equation Using the Riemann–Stieltjes Integral Boundary Condition," Mathematics, MDPI, vol. 13(3), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:541-:d:1585115
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