Browsing by Author "El-Deeb, Ahmed A."

Now showing 1 - 19 of 19

Citation - WoS: 9
Citation - Scopus: 8
A variety of dynamic α-conformable Steffensen-type inequality on a time scale measure space
(Amer inst Mathematical Sciences-aims, 2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Moaaz, Osama; Baleanu, Dumitru; Askar, Sameh S.; 56389
The main objective of this work is to establish several new alpha-conformable of Steffensen-type inequalities on time scales. Our results will be proved by using time scales calculus technique. We get several well-known inequalities due to Steffensen, if we take alpha = 1. Some cases we get continuous inequalities when T = R and discrete inequalities when T = Z.
Citation - WoS: 0
Citation - Scopus: 1
Bennett-Leindler nabla type inequalities via conformable fractional derivatives on time scales
(Amer inst Mathematical Sciences-aims, 2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Makharesh, Samer D.; Askar, Sameh S.; Baleanu, Dumitru; 56389
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.
Citation - WoS: 2
Citation - Scopus: 1
Diamond Alpha Hilbert-Type Inequalities on Time Scales
(Mdpi, 2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Baleanu, Dumitru; Askar, Sameh S.; Cesarano, Clemente; Abdeldaim, Ahmed; 56389
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.
Citation - WoS: 15
Citation - Scopus: 18
Dynamic Hilbert-Type Inequalities with Fenchel-Legendre Transform
(Mdpi, 2020) El-Deeb, Ahmed A.; Baleanu, Dumitru; Makharesh, Samer D.; Baleanu, Dumitru; 56389
Our work is based on the multiple inequalities illustrated in 2020 by Hamiaz and Abuelela. With the help of a Fenchel-Legendre transform, which is used in various problems involving symmetry, we generalize a number of those inequalities to a general time scale. Besides that, in order to get new results as special cases, we will extend our results to continuous and discrete calculus.
Citation - WoS: 7
Citation - Scopus: 7
Generalization Of Mitrinović–Pečarić Inequalities On Time Scales
(Rocky Mt Math Consortium, 2021) El-Deeb, Ahmed A.; Kaymakçalan, Billur; Akin, Elvan; Kaymakcalan, Billur; 109448
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.
Citation - WoS: 7
Citation - Scopus: 8
New Weighted Opial-Type Inequalities on Time Scales for Convex Functions
(Mdpi, 2020) El-Deeb, Ahmed A.; Baleanu, Dumitru; Baleanu, Dumitru; 56389
Our work is based on the multiple inequalities illustrated in 1967 by E. K. Godunova and V. I. Levin, in 1990 by Hwang and Yang and in 1993 by B. G. Pachpatte. With the help of the dynamic Jensen and Holder inequality, we generalize a number of those inequalities to a general time scale. In addition to these generalizations, some integral and discrete inequalities will be obtained as special cases of our results.
Citation - WoS: 0
Citation - Scopus: 0
On Hardy-Hilbert-type inequalities with α-fractional derivatives
(Amer inst Mathematical Sciences-aims, 2023) Ahmed, Marwa M.; Baleanu, Dumitru; Hassanein, Wael S.; Elsayed, Marwa Sh.; Baleanu, Dumitru; El-Deeb, Ahmed A.; 56389
In the current manuscript, new alpha delta dynamic Hardy-Hilbert inequalities on time scales are discussed. These inequalities combine and expand a number of continuous inequalities and their corresponding discrete analogues in the literature. We shall illustrate our results using Holder's inequality on time scales and a few algebraic inequalities.
Citation - WoS: 9
Citation - Scopus: 8
On nabla conformable fractional Hardy-type inequalities on arbitrary time scales
(Springer, 2021) El-Deeb, Ahmed A.; Baleanu, Dumitru; Makharesh, Samer D.; Nwaeze, Eze R.; Iyiola, Olaniyi S.; Baleanu, Dumitru; 56389
The main aim of the present article is to introduce some new backward difference -conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini's theorem on time scales. Our results generalize, complement, and extend existing results in the literature. Many special cases of the proposed results, such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities, and new classical conformable fractional integral inequalities, are obtained and analyzed.
Citation - WoS: 0
Citation - Scopus: 0
On some dynamic inequalities of Hilbert’s-type on time scales
(Amer inst Mathematical Sciences-aims, 2023) El-Deeb, Ahmed A.; Baleanu, Dumitru; Baleanu, Dumitrru; Shah, Nehad Ali; Abdeldaim, Ahmed; 56389
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.
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: 1
Citation - Scopus: 0
On Some Important Class of Dynamic Hilbert’s-Type Inequalities on Time Scales
(Mdpi, 2022) El-Owaidy, Hassan M.; Baleanu, Dumitru; El-Deeb, Ahmed A.; Makharesh, Samer D.; Baleanu, Dumitru; Cesarano, Clemente; 56389
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.
Citation - WoS: 1
Citation - Scopus: 0
On Some Important Dynamic Inequalities of Hardy-Hilbert on Timescales
(Mdpi, 2022) Baleanu, Dumitru; Baleanu, Dumitru; Cesarano, Clemente; Abdeldaim, Ahmed
In 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.
Citation - WoS: 0
Citation - Scopus: 0
Some Generalizations of Novel (Δ backward difference )Δ-Gronwall-Pachpatte Dynamic Inequalities on Time Scales with Applications
(Mdpi, 2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Baleanu, Dumitru; 56389
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.
Citation - WoS: 11
Citation - Scopus: 11
Some new dynamic Gronwall-Bellman-Pachpatte type inequalities with delay on time scales and certain applications
(Springer, 2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Baleanu, Dumitru; 56389
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.
Citation - WoS: 20
Citation - Scopus: 24
Some new Hardy-type inequalities on time scales
(Springer, 2020) El-Deeb, Ahmed A.; Baleanu, Dumitru; Elsennary, Hamza A.; Baleanu, Dumitru; 56389
In this paper, we will prove some new dynamic inequalities of Hardy-type on time scales. Some of the integral and difference inequalities that will be derived from our results in the continuous and discrete cases are original. The main results will be proved by using the dynamic Holder inequality, integration by parts formula on time scales, and Keller's chain rule on time scales. We will apply the main results to the continuous calculus, discrete calculus, and q-calculus as special cases.
Citation - WoS: 1
Citation - Scopus: 1
Weighted Dynamic Hardy-Type Inequalities Involving Many Functions on Arbitrary Time Scales
(Springer, 2022) Baleanu, Dumitru; 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.
Citation - WoS: 0
Citation - Scopus: 0
(γ,a)-Nabla Reverse Hardy–Hilbert-Type Inequalities on Time Scales
(Mdpi, 2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Baleanu, Dumitru; Awrejcewicz, Jan; 56389
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.
Citation - WoS: 0
Citation - Scopus: 0
Δ-Gronwall Dynamic Inequalities and Their Applications on Time Scales
(Mdpi, 2022) Baleanu, Dumitru; Baleanu, Dumitru; Awrejcewicz, Jan
In 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.
Citation - WoS: 2
Citation - Scopus: 3
(Δ∇)∇-Pachpatte Dynamic Inequalities Associated with Leibniz Integral Rule on Time Scales with Applications
(Mdpi, 2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Baleanu, Dumitru; Awrejcewicz, Jan; 56389
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.