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

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of science, University of Jeddah, Jeddah, 21589, Saudi Arabia Cairo University, Department of Mathematics, Giza, Egypt

2 Department 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