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Existence of solutions of BVPs for fractional Langevin equations involving Caputo fractional derivatives

  • Zohre Kiyamehr and Hamid Baghani EMAIL logo
Published/Copyright: December 11, 2020

Abstract

This article investigates a nonlinear fractional Caputo–Langevin equation

Dβ(Dα+λ)x(t)=f(t,x(t)),0<t<1, 0<α1, 1<β2,

subject to the multi-point boundary conditions

x(0)=0,𝒟2αx(1)+λ𝒟αx(1)=0,x(1)=0ηx(τ)𝑑τfor some 0<η<1,

where Dα is the Caputo fractional derivative of order α, f:[0,1]× is a given continuous function, and λ is a real number. Some new existence and uniqueness results are obtained by applying an interesting fixed point theorem.

MSC 2010: 26A33; 34A08; 34A12

References

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Received: 2019-01-08
Revised: 2019-11-16
Accepted: 2019-12-02
Published Online: 2020-12-11
Published in Print: 2021-06-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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