Stability analysis of nonlinear implicit fractional Langevin equation with noninstantaneous impulses

In this paper, we consider a nonlocal boundary value problem of nonlinear implicit fractional Langevin equation with noninstantaneous impulses. We study the existence, uniqueness and generalized Ulam–Hyers–Rassias stability of the proposed model with the help of fixed point approach, over generalize...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2019; no. 1; pp. 1 - 31
Main Authors Rizwan, Rizwan, Zada, Akbar, Wang, Xiaoming
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2019
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Boundary value problems
Caputo derivative
Difference and Functional Equations
Functional Analysis
Implicit Langevin equation
Impulses
Mathematics
Mathematics and Statistics
Metric space
noninstantaneous impulses
Nonlinear analysis
Ordinary Differential Equations
Partial Differential Equations
Stability analysis
Ulam–Hyers–Rassias stability
34B27
Caputo derivative
noninstantaneous impulses
Ulam–Hyers–Rassias stability
26A33
Implicit Langevin equation
34A08
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Summary:In this paper, we consider a nonlocal boundary value problem of nonlinear implicit fractional Langevin equation with noninstantaneous impulses. We study the existence, uniqueness and generalized Ulam–Hyers–Rassias stability of the proposed model with the help of fixed point approach, over generalized complete metric space. We give an example which supports our main result.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-1955-1