Local existence–uniqueness and monotone iterative approximation of positive solutions for p-Laplacian differential equations involving tempered fractional derivatives

• Published in: Journal of inequalities and applications Vol. 2021; no. 1; pp. 1 - 16
• Main Authors: Zhou, Bibo, Zhang, Lingling
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 28.09.2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Approximation; Boundary value problems; Control theory; Differential equations; Existence and uniqueness; Fixed points (mathematics); Mathematics; Mathematics and Statistics; Operators (mathematics); p-Laplacian operator; Random variables; Riemann–Stieltjes integral boundary value conditions; Stieltjes integral; Sum-type mixed monotone operator; Tempered fractional derivative; Uniqueness; Sum-type mixed monotone operator; Tempered fractional derivative; Riemann–Stieltjes integral boundary value conditions; 35J05; Existence and uniqueness; Laplacian operator; 34B18; 34A08
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-021-02693-w

In this paper, we are concerned with a kind of tempered fractional differential equation Riemann–Stieltjes integral boundary value problems with p -Laplacian operators. By means of the sum-type mixed monotone operators fixed point theorem based on the cone P h , we obtain not only the local existence with a unique positive solution, but also construct two successively monotone iterative sequences for approximating the unique positive solution. Finally, we present an example to illustrate our main results.