Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Population Dynamic Caused by War Involvement via Fractional Derivative on Time Scales(Inderscience Publishers, 2019) Baleanu, Dumitru; Agheli, Bahram; Neamaty, Abdolali; Nategh, MehdiArticle Citation - Scopus: 2Non-Integer Variable Order Dynamic Equations on Time Scales Involving Caputo-Fabrizio Type Differential Operator(Eudoxus Press, LLC, 2018) Baleanu, D.; Baleanu, Dumitru; Nategh, M.; MatematikThis work deals with the conecept of a Caputo-Fabrizio type non-integer variable order differential opertor on time scales that involves a non-singular kernel. A measure theoretic discussion on the limit cases for the order of differentiation is presented. Then, corresponding to the fractional derivative, we discuss on an integral for constant and variable orders. Beside the obtaining solutions to some dynamic problems on time scales involving the proposed derivative, a fractional folrmulation for the viscoelastic oscillation problem is studied and its conversion into a third order dynamic equation is presented. © 2018 by Eudoxus Press, LLC. All rights reserved.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 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 - 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.