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Connections between Ulam-Hyers Stability and Uniform Exponential Stability of Time Varying Linear Dynamic Systems Over Time Scales |
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PP: 1-4 |
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doi:10.18576/sjm/060101
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Author(s) |
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Syed Omar Shah,
Akbar Zada,
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Abstract |
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| In this paper, we prove that the regressive time varying linear dynamic equation xD (r) = G(r)x(r), r ∈ T is Ulam–Hyers
stable if and only if it is uniformly exponentially stable. Furthermore, the Ulam–Hyers stability and uniform exponential stability of the
system xD (r) = G(r)x(r), r ∈ T is proved in terms of bounded-ness of solution of the following Cauchy problem:
(
WD (r) = G(r)W(r)+w(r), 0 ≤ r ∈ T,
W(0) = v0,
where T denotes time scale, G(r) is a matrix valued function, w(r) is a bounded function on T and v0 ∈ Cm. |
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