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Stability by Krasnoselskii’s fixed point theorem for nonlinear fractional dynamic equations on a time scale. (English) Zbl 1459.34166

Summary: In this paper, we give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of nonlinear fractional dynamic equations of order \({\alpha}\) \((1 < {\alpha} < 2)\). By using the Krasnoselskii’s fixed point theorem in a weighted Banach space, we establish new results on the asymptotic stability of the zero solution provided \(f (t, 0) = 0\), which include and improve some related results in the literature.

MSC:

34K20 Stability theory of functional-differential equations
34N05 Dynamic equations on time scales or measure chains
47N20 Applications of operator theory to differential and integral equations
34K37 Functional-differential equations with fractional derivatives
34K42 Functional-differential equations on time scales or measure chains
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