Stability of Ulam–Hyers and Existence of Solutions for Impulsive Time-Delay Semi-Linear Systems with Non-Permutable Matrices

Nazim I. Mahmudov and Amal M. Almatarneh
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Nazim I. Mahmudov: Department of Mathematics, Eastern Mediterranean University, Famagusta 99628, T.R. North Cyprus Mersin 10, Turkey
Amal M. Almatarneh: Department of Mathematics, Eastern Mediterranean University, Famagusta 99628, T.R. North Cyprus Mersin 10, Turkey

Mathematics, 2020, vol. 8, issue 9, 1-17

Abstract: In this paper, the stability of Ulam–Hyers and existence of solutions for semi-linear time-delay systems with linear impulsive conditions are studied. The linear parts of the impulsive systems are defined by non-permutable matrices. To obtain solution for linear impulsive delay systems with non-permutable matrices in explicit form, a new concept of impulsive delayed matrix exponential is introduced. Using the representation formula and norm estimation of the impulsive delayed matrix exponential, sufficient conditions for stability of Ulam–Hyers and existence of solutions are obtained.

Keywords: impulsive delay equation; delayed matrix exponential; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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