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

Abstract

Abstract 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 $P_{h}$ , 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.

Keywords

• Tempered fractional derivative
• p-Laplacian operator
• Sum-type mixed monotone operator
• Existence and uniqueness
• Riemann–Stieltjes integral boundary value conditions