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Please use this identifier to cite or link to this item: http://hdl.handle.net/11129/6463

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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