New existence and stability results for fractional Langevin equation with three-point boundary conditions

چکیده مقاله

The aim of the paper is to present a new technical analysis of the special case of the nonlinear Langevin equation with positive friction constant involving two fractional orders with three-point boundary conditions. Using some basic properties of the special case of the Prabhakar integral operator, we find an equivalent integral equation to the mentioned equation. We obtain a new result on existence, uniqueness and Hyers–Ulam stability by employing contraction mapping principle and Krasnoselskii’s fixed point theorem with respect to an appropriate weighted Banach space. Our result is an improvement of existing results reported in the previous literature. The consistency of the main results is demonstrated by some examples. © 2021, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.