Hamza, A., Ismail, G., Ahmed, D. (2017). Many Types of Stability of Abstract First and Second Order Linear Dynamic Equations on Time Scales. test, 34(part1), 19-32. doi: 10.21608/jsrs.2018.12748
Alaa E. Hamza; Gamal . A.F. Ismail; Dina Ahmed. "Many Types of Stability of Abstract First and Second Order Linear Dynamic Equations on Time Scales". test, 34, part1, 2017, 19-32. doi: 10.21608/jsrs.2018.12748
Hamza, A., Ismail, G., Ahmed, D. (2017). 'Many Types of Stability of Abstract First and Second Order Linear Dynamic Equations on Time Scales', test, 34(part1), pp. 19-32. doi: 10.21608/jsrs.2018.12748
Hamza, A., Ismail, G., Ahmed, D. Many Types of Stability of Abstract First and Second Order Linear Dynamic Equations on Time Scales. test, 2017; 34(part1): 19-32. doi: 10.21608/jsrs.2018.12748

Many Types of Stability of Abstract First and Second Order Linear Dynamic Equations on Time Scales

Journal of Scientific Research in Science
Article 2, Volume 34, part1, September 2017, Pages 19-32    PDF (696.85 K)
Document Type: Original Article
DOI: 10.21608/jsrs.2018.12748
Authors
Alaa E. Hamza1; Gamal . A.F. Ismail2; Dina Ahmed* 2
1Department of Mathematics, Faculty of science, University of Jeddah, Jeddah, 21589, Saudi Arabia Cairo University, Department of Mathematics, Giza, Egypt
2Department of Mathematics, Faculty of Girls, Ain Shams University, Cairo, Egypt
Abstract
In this paper we investigate sufficient conditions for many types of stability of both of the abstract first order linear dynamic equations on time scales of the form
 
and the second order linear dynamic equations of the form
 
Where , the space of all bounded linear operators from a Banachspace 𝕏 into itself, and  is rd–continuous from a time scale 𝕋to 𝕏. Some givenillustrative examples show the applicability of the main results.
Mathematics Subject Classifications:26E70, 34N05, 34K20, 39A30.
 
Keywords
Time scales; Linear dynamic equations; Stability theory
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