Dynamic Hardy–Copson-Type Inequalities via (γ,a)-Nabla-Conformable Derivatives on Time Scales

El‐Deeb, Ahmed A.; Makharesh, Samer D.; Awrejcewicz, Jan; Agarwal, Ravi P.

doi:10.3390/sym14091847

Cited by 4 publications

(2 citation statements)

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“…In [14], El-Deeb et al proved that if 0 ≤ x ∈ T, δ ≥ a, then Ω and ϕ are nonnegative (γ, a)-nabla fractional differentiable and locally integrable functions on…”

Section: Introductionmentioning

confidence: 99%

Generalized Dynamic Inequalities of Copson Type on Time Scales

Ahmed,

Saied,

Ali

et al. 2024

Symmetry

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This paper introduces novel generalizations of dynamic inequalities of Copson type within the framework of time scales delta calculus. The proposed generalizations leverage mathematical tools such as Hölder’s inequality, Minkowski’s inequality, the chain rule on time scales, and the properties of power rules on time scales. As special cases of our results, particularly when the time scale T equals the real line (T=R), we derive some classical continuous analogs of previous inequalities. Furthermore, when T corresponds to the set of natural numbers including zero (T=N0), the obtained results, to the best of the authors’ knowledge, represent innovative contributions to the field.

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“…In [14], El-Deeb et al proved that if 0 ≤ x ∈ T, δ ≥ a, then Ω and ϕ are nonnegative (γ, a)-nabla fractional differentiable and locally integrable functions on…”

Section: Introductionmentioning

confidence: 99%

Generalized Dynamic Inequalities of Copson Type on Time Scales

Ahmed,

Saied,

Ali

et al. 2024

Symmetry

View full text Add to dashboard Cite

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“…Wendroff's inequality (Inequality (4)) has gained significant attention, and numerous articles have been published in the literature involved various extensions, generalizations, and applications [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

On Some Generalizations of Integral Inequalities in n Independent Variables and Their Applications

Abuelela

El‐Deeb²,

Băleanu³

2022

Symmetry

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Throughout this article, generalizations of some Grónwall–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.

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