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 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 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 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.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: 69Citation - Scopus: 68New Applications of the Variational Iteration Method - From Differential Equations To Q-Fractional Difference Equations(Springeropen, 2013) Baleanu, Dumitru; Wu, Guo-ChengThe non-classical calculi such as q-calculus, fractional calculus and q-fractional calculus have been hot topics in both applied and pure sciences. Then some new linear and nonlinear models have appeared. This study mainly concentrates on the analytical aspects, and the variational iteration method is extended in a new way to solve an initial value problem.Article Citation - WoS: 6Citation - Scopus: 14Generalized Diamond-Α Dynamic Opial Inequalities(Springer, 2012) Lesaja, Goran; Tas, Kenan; Atasever, Nuriye; Kaymakcalan, BillurWe establish some new dynamic Opial-type diamond alpha inequalities in time scales. Our results in special cases yield some of the recent results on Opial's inequality and also provide new estimates on inequalities of this type. Also, we introduce an example to illustrate our result.