Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
