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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Angheluta-Bauer, Luiza / Chen, Xi / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi / Yang, Xu

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Volume 20, Issue 7-8


Existence Theory and Stability Analysis of Fractional Langevin Equation

Rizwan Rizwan
  • Corresponding author
  • Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan
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Published Online: 2019-08-20 | DOI: https://doi.org/10.1515/ijnsns-2019-0053


In this paper, we consider a non local boundary value problem of nonlinear fractional Langevin equation with non-instantaneous impulses. Initially, we form a standard framework to originate a formula of solutions to our proposed model and then implement the concept of generalized Ulam–Hyers–Rassias using Diaz–Margolis’s fixed point theorem over a generalized complete metric space.

Keywords: Langevin equation; Caputo derivative; impulse; Ulam–Hyers–Rassias stability

MSC 2010: 26A33; 34A08; 34B27


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About the article

Received: 2019-02-07

Accepted: 2019-07-22

Published Online: 2019-08-20

Published in Print: 2019-11-18

Competing interests The authors declare that they have no competing interest regarding this research work.

Authors contributions All the authors contributed equally and significantly in writing this paper. All the authors read and approved the final manuscript.

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 20, Issue 7-8, Pages 833–848, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2019-0053.

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