Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 5Citation - Scopus: 5Weighted Dynamic Hardy-Type Inequalities Involving Many Functions on Arbitrary Time Scales(Springer, 2022) El-Deeb, Ahmed A.; Mohamed, Karim A.; Baleanu, Dumitru; Rezk, Haytham M.The objective of this paper is to prove some new dynamic inequalities of Hardy type on time scales which generalize and improve some recent results given in the literature. Further, we derive some new weighted Hardy dynamic inequalities involving many functions on time scales. As special cases, we get continuous and discrete inequalities.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 Citation - WoS: 4Citation - Scopus: 4Some New Dynamic Inequalities With Several Functions of Hardy Type on Time Scales(Springer, 2021) Abuelela, Waleed; Saker, Samir H.; Baleanu, Dumitru; Hamiaz, AdnaneThe aim of this article is to prove some new dynamic inequalities of Hardy type on time scales with several functions. Our results contain some results proved in the literature, which are deduced as limited cases, and also improve some obtained results by using weak conditions. In order to do so, we utilize Holder's inequality, the chain rule, and the formula of integration by parts on time scales.Article Citation - WoS: 11Citation - Scopus: 13Some New Dynamic Gronwall-Bellman Type Inequalities With Delay on Time Scales and Certain Applications(Springer, 2022) Baleanu, Dumitru; El-Deeb, Ahmed A.The main objective of the present article is to prove some new delay nonlinear dynamic inequalities of Gronwall-Bellman-Pachpatte type on time scales. We introduce very important generalized results with the help of Leibniz integral rule on time scales. For some specific time scales, we further show some relevant inequalities as special cases: integral inequalities and discrete inequalities. Our results can be used as handy tools for the study of qualitative and quantitative properties of solutions of dynamic equations on time scales. Some examples are provided to demonstrate the applications of the results.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 - WoS: 4Citation - Scopus: 5Derivation of Dynamical Integral Inequalities Based on Two-Dimensional Time Scales Theory(Springer, 2020) Khan, Hasib; Khan, Zareen A.; Jarad, Fahd; Khan, AzizThe main goal of this paper is to set up some new estimates of a specific class of dynamic integral inequalities (DII) which are partially linear on a time scale T with two independent variables. These, from the one hand, sum up and, on the other hand, offer a helpful method for both the qualitative and quantitative study of dynamic equations on time scales. Some applications are taken into consideration to show the validity of the fundamental results.Article Citation - WoS: 24Citation - Scopus: 19Refinement Multidimensional Dynamic Inequalities With General Kernels and Measures(Springeropen, 2019) Rezk, Haytham M.; Abohela, Islam; Baleanu, Dumitru; Saker, Samir H.Using the properties of superquadratic and subquadratic functions, we establish some new refinement multidimensional dynamic inequalities of Hardy's type on time scales. Our results contain some of the recent results related to classical multidimensional Hardy's and Polya-Knopp's inequalities on time scales. To show motivation of the paper, we apply our results to obtain some particular multidimensional cases and provide refinements of some Hardy-type inequalities known in the literature.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.