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Ulam type stability for non-instantaneous impulsive Caputo fractional differential equations with finite state dependent delay

Ulam type stability for non-instantaneous impulsive Caputo fractional differential equations with... AbstractFour Ulam type stability concepts for non-instantaneous impulsive fractionaldifferential equations with state dependent delay are introduced. Two different approaches to the interpretation of solutions are investigated. We study the case of an unchangeable lower bound of the Caputo fractional derivative and the case of a lower bound coinciding with the point of jump for the solution. In both cases we obtain sufficient conditions for Ulam type stability. An example is also provided to illustrate both approaches. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Ulam type stability for non-instantaneous impulsive Caputo fractional differential equations with finite state dependent delay

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Publisher
de Gruyter
Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
DOI
10.1515/gmj-2020-2061
Publisher site
See Article on Publisher Site

Abstract

AbstractFour Ulam type stability concepts for non-instantaneous impulsive fractionaldifferential equations with state dependent delay are introduced. Two different approaches to the interpretation of solutions are investigated. We study the case of an unchangeable lower bound of the Caputo fractional derivative and the case of a lower bound coinciding with the point of jump for the solution. In both cases we obtain sufficient conditions for Ulam type stability. An example is also provided to illustrate both approaches.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Aug 1, 2021

Keywords: Caputo fractional differential equations; state dependent delays; non-instantaneous impulses; existence; Ulam type stability; 34K20; 34K37; 34K45

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