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Title: | Existence and Controllability of Conformable Impulsive Equations |
Authors: | Mahmudov, Nazim (Supervisor) Akgün, Gülbahar Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics |
Keywords: | Thesis Tez Applied Mathematics and Computer Science Mathematics Department Impulsive Equations Impulsive differential equations Existence theorems |
Issue Date: | Dec-2023 |
Publisher: | Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ) |
Citation: | Akgün, Gülbahar. (2023). Existence and Controllability of Conformable Impulsive Equations . Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus. |
Abstract: | In this study, the focus is directed towards the explanation of existence and uniqueness
phenomena in impulsive dynamical systems governed by conformable fractional
nonlinear differential equations. Concurrently, the analysis encompasses the
controllability of systems delineated by linear and semilinear conformable fractional
impulsive control mechanisms. By utilizing the mathematical apparatus of
conformable fractional derivatives, salient constructs such as the conformable
controllability operator and the conformable controllability Gramian matrix are
introduced. These instrumentalities facilitate the derivation of both necessary and
sufficient conditions that are requisite for achieving comprehensive controllability in
linear impulsive systems within the framework of conformable fractional calculus.
Moreover, an assemblage of rigorously formulated sufficient criteria is prefered to
ascertain the controllability of semilinear impulsive systems in the domain of
conformable fractional calculus. ÖZ:
Bu çalışmada, odak noktası, uyumlu kesirli tip dürtüsel olmayan diferansiyel
denklemlerle yönetilen sistemlerde varlık ve benzersizlik olgularının açıklanmasına
yöneliktir. Aynı anda, analiz, doğrusal ve yarı doğrusal uyumlu kesirli ani kontrol
mekanizmaları tarafından belirlenen sistemlerin kontrol edilebilirliğini kapsar.
Uyumlu kesirli türevlerin matematik araçlarını kullanarak, uyumlu kontrol edilebilirlik
operatörü ve uyumlu kontrol edilebilirlik Gramian matrisi gibi önemli yapılar
tanıtılmıştır. Bu araçlar, uyumlu kesirli hesaplamalar çerçevesinde doğrusal
sistemlerde kapsamlı kontrol edilebilirlik için gerekli olan hem gerekli hem de yeterli
koşulların türetilmeyi kolaylaştırır. Ayrıca, uyumlu kesirli hesaplamalar alanında yarı
doğrusal sistemlerin kontrol edilebilirliğini belirlemek için sıkıca formüle edilmiş
yeterli kriterlerin bir derlemesi sunulmaktadır. |
Description: | Doctor of Philosophy in Applied Mathematics and Computer Science. Institute of Graduate Studies and Research. Thesis (Ph.D.) - Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2023. Supervisor: Prof. Dr. Prof. Dr. Nazim Mahmudov. |
URI: | http://hdl.handle.net/11129/6463 |
Appears in Collections: | Theses (Master's and Ph.D) – Mathematics
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