Browsing by Author "Abuelela, Waleed"

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Citation - WoS: 1
Citation - Scopus: 0
On Some Generalizations of Integral Inequalities in n Independent Variables and Their Applications
(Mdpi, 2022) Abuelela, Waleed; Baleanu, Dumitru; El-Deeb, Ahmed A.; Baleanu, Dumitru; 56389
Throughout this article, generalizations of some Gronwall-Bellman integral inequalities for two real-valued unknown functions in n independent variables are introduced. We are looking at some novel explicit bounds of a particular class of Young and Pachpatte integral inequalities. The results in this paper can be utilized as a useful way to investigate the uniqueness, boundedness, continuousness, dependence and stability of nonlinear hyperbolic partial integro-differential equations. To highlight our research advantages, several implementations of these findings will be presented. Young's method, which depends on a Riemann method, will follow to prove the key results. Symmetry plays an essential role in determining the correct methods for solving dynamic inequalities.
Citation - WoS: 2
Citation - Scopus: 2
Some new dynamic inequalities with several functions of Hardy type on time scales
(Springer, 2021) Hamiaz, Adnane; Baleanu, Dumitru; Abuelela, Waleed; Saker, Samir H.; Baleanu, Dumitru; 56389
The 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.