Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article New Weighted Opial-Type Inequalities on Time Scales for Convex Functions(MDPI AG, 2020) Baleanu, Dumitru; El-Deeb, Ahmed A.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: 1On Some Important Dynamic Inequalities of Hardy-Hilbert on Timescales(Mdpi, 2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Cesarano, Clemente; Abdeldaim, AhmedIn this article, by using some algebraic inequalities, nabla Holder inequalities, and nabla Jensen's inequalities on timescales, we proved some new nabla Hilbert-type dynamic inequalities on timescales. These inequalities extend some known dynamic inequalities on timescales and unify some continuous inequalities and their corresponding discrete analogues. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.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: 1On Some Important Class of Dynamic Hilbert's-type Inequalities on Time Scales(Mdpi, 2022) El-Deeb, Ahmed A.; Makharesh, Samer D.; Baleanu, Dumitru; Cesarano, Clemente; El-Owaidy, Hassan M.In this important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The inequalities investigated here generalize several known dynamic inequalities on time scales and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using some algebraic inequalities, Holder inequality, and Jensen's inequality on time scales.Article Citation - WoS: 7Citation - Scopus: 7Generalization of Mitrinovic-Pecaric Inequalities on Time Scales(Rocky Mt Math Consortium, 2021) Akin, Elvan; Kaymakcalan, Billur; El-Deeb, Ahmed A.We prove some new inequalities of Mitrinovic-Pecaric inequalities for convex functions on an arbitrary time scale using delta integrals. These inequalities extend and improve some known dynamic inequalities in the literature. The main results will be proved by using Holder and Jensen inequalities and a simple consequence of Keller's and Poetzsche's chain rules on time scales.Article Citation - WoS: 2Citation - Scopus: 1Diamond Alpha Hilbert-Type Inequalities on Time Scales(Mdpi, 2022) Baleanu, Dumitru; Askar, Sameh S.; Cesarano, Clemente; Abdeldaim, Ahmed; El-Deeb, Ahmed A.In this article, we will prove some new diamond alpha Hilbert-type dynamic inequalities on time scales which are defined as a linear combination of the nabla and delta integrals. These inequalities extend some known dynamic inequalities on time scales, and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proven by using some algebraic inequalities, diamond alpha Holder inequality, and diamond alpha Jensen's inequality on time scales.Article Citation - Scopus: 1Bennett-Leindler Nabla Type Inequalities Via Conformable Fractional Derivatives on Time Scales(Amer inst Mathematical Sciences-aims, 2022) Makharesh, Samer D.; Askar, Sameh S.; Baleanu, Dumitru; El-Deeb, Ahmed A.In this work, we prove several new (gamma, a)-nabla Bennett and Leindler dynamic inequalities on time scales. The results proved here generalize some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using integration by parts, chain rule and Holder inequality for the (gamma, a)-nabla-fractional derivative on time scales.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 On Some Dynamic Inequalities of Hilbert's-type on Time Scales(Amer inst Mathematical Sciences-aims, 2023) Baleanu, Dumitrru; Shah, Nehad Ali; Abdeldaim, Ahmed; El-Deeb, Ahmed A.In this article, we will prove some new conformable fractional Hilbert-type dynamic inequalities on time scales. These inequalities generalize some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using some algebraic inequalities, conformable fractional Ho center dot lder inequalities, and conformable fractional Jensen's inequalities on time scales.