Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 14Citation - Scopus: 19On the Discrete Sumudu Transform(Editura Acad Romane, 2012) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Bayram, Kamm; Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru; Köse, Hasan; Ameen, Raad; MatematikIn this paper, we define the Sumudu transform on an arbitrary time scale. Starting from this definition we define the discrete Sumudu transform. We prove the initial and final value problems and study the basic properties of this transform. We also present the discrete Sumudu transform of some basic functions.Article Δ-Gronwall Dynamic Inequalities and Their Applications on Time Scales(Mdpi, 2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Awrejcewicz, JanIn this article, with the help of Leibniz integral rule on time scales, we prove some new dynamic inequalities of Gronwall-Bellman-Pachpatte-type on time scales. These inequalities can be used as handy tools to study the qualitative and quantitative properties of solutions of the initial boundary value problem for partial delay dynamic equation.Article Some Generalizations of Novel (Δ Backward Difference )<sup>δ</Sup>-gronwall-pachpatte Dynamic Inequalities on Time Scales With Applications(Mdpi, 2022) Baleanu, Dumitru; El-Deeb, Ahmed A.We established several novel inequalities of Gronwall-Pachpatte type on time scales. Our results can be used as handy tools to study the qualitative and quantitative properties of the solutions of the initial boundary value problem for a partial delay dynamic equation. The Leibniz integral rule on time scales has been used in the technique of our proof. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.Article Citation - WoS: 2Citation - Scopus: 3(Δ Backward Difference )<sup> Backward Difference </Sup>-pachpatte Dynamic Inequalities Associated With Leibniz Integral Rule on Time Scales With Applications(Mdpi, 2022) Baleanu, Dumitru; Awrejcewicz, Jan; El-Deeb, Ahmed A.We prove some new dynamic inequalities of the Gronwall-Bellman-Pachpatte type on time scales. Our results can be used in analyses as useful tools for some types of partial dynamic equations on time scales and in their applications in environmental phenomena and physical and engineering sciences that are described by partial differential equations.Article (γ,a)-Nabla Reverse Hardy-Hilbert Inequalities on Time Scales(Mdpi, 2022) Baleanu, Dumitru; Awrejcewicz, Jan; El-Deeb, Ahmed A.In this article, using a (gamma,a)-nabla conformable integral on time scales, we study several novel Hilbert-type dynamic inequalities via nabla time scales calculus. Our results generalize various inequalities on time scales, unifying and extending several discrete inequalities and their corresponding continuous analogues. We say that symmetry plays an essential role in determining the correct methods with which to solve dynamic inequalities.Article Citation - Scopus: 3Oscillation for a Nonlinear Dynamic System on Time Scales(2011) Mert, R.; Erbe, L.We study the oscillation properties of a system of two first-order nonlinear equations on time scales. This form includes the classical Emden-Fowler differential and difference equations and many of its extensions. We generalize some well-known results of Atkinson, Belohorec, Waltman, Hooker, Patula and others and also describe the relation to solutions of a delay-dynamic system. © 2011 Taylor & Francis.Article Citation - WoS: 6Citation - Scopus: 6Singular Multiparameter Dynamic Equations With Distributional Potentials on Time Scales(Natl inquiry Services Centre Pty Ltd, 2017) Ugurlu, EkinIn this paper, we consider both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-infinite time scales. At first we construct Weyls theory for the single singular multiparameter dynamic equation with distributional potentials and we prove that the forward jump of at least one solution of this equation must be squarely integrable with respect to some multiple function which is of one sign and nonzero on the given time scale. Then using the obtained results for the single dynamic equation with several parameters, we investigate the number of the products of the squarely integrable solutions of the singular several equations with distributional potentials and several parameters.