Nonlinear impulsive Langevin equation with mixed derivatives

In this paper, we consider a nonlocal boundary value problem of nonlinear impulsive Langevin equation with mixed derivatives. Some sufficient conditions are constructed to observe the existence, uniqueness, and generalized Ulam‐Hyers‐Rassias stability of our proposed model, with the help of Diaz‐Mar...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-01, Vol.43 (1), p.427-442
Main Authors: Rizwan, Rizwan, Zada, Akbar
Format: Article
Language:English
Subjects:
Boundary value problems
Caputo derivative
Derivatives
Langevin equation
Metric space
noninstantaneous impulses
Ulam‐Hyers‐Rassias stability
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Summary:In this paper, we consider a nonlocal boundary value problem of nonlinear impulsive Langevin equation with mixed derivatives. Some sufficient conditions are constructed to observe the existence, uniqueness, and generalized Ulam‐Hyers‐Rassias stability of our proposed model, with the help of Diaz‐Margolis' fixed‐point approach over generalized complete metric space. We give an example that supports our main result.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5902