A. A. Abdelhakim

activity

20152025

most citedThe flaw in the conformable calculus: it is conformable because it is not fractional

106 citations · 213 across the 11 of their papers we have counts for

collaborators

13 papers

math.CA2025

A Littlewood-Paley approach to the Mittag-Leffler function in the frequency space and applications to nonlocal problems

Ahmed A. Abdelhakim

Let $0 < α < 2$ , $β > 0$ and $α /2 < ∣ s ∣ \leq 1$ . In a previous work, we obtained all possible values of the Lebesgue exponent $p = p (γ)$ for which the Fourier transform of $ E_{α,β}(e^{\dot{\…

math.CA2024

On the asymptotic behaviour of the Fourier transform of the Mittag-Leffler function

Ahmed A. Abdelhakim

Let $α \in (0, 2)$ and let $β > 0$ . Fix $- π < φ \leq π$ such that $∣ φ ∣ > α π /2$ . We obtain asymptotic upper bounds on the Fourier transform of the radially symmetric tempered distribution \b…

math.FA2020

Optimal critical exponent $L^{p}$ inequalities of Hardy type on the sphere via Xiao's method

Ahmed A. Abdelhakim

First, we correct the proof presented in [Abimbola Abolarinwa, Kamilu Rauf, Songting Yin, Sharp $L^{p}$ Hardy type and uncertainty principle inequalities on the sphere, Journal of…

math.FA2020

Sharp subcritical and critical $L^{p}$ Hardy inequalities on the sphere

Ahmed A. Abdelhakim

We prove sharp inequalities of Hardy type for functions in the Sobolev space $W^{1, p}$ on the unit sphere $S^{n - 1}$ in $R^{n}$ . We achieve this in both the subcri…

math.CA2018★ 106 cited

The flaw in the conformable calculus: it is conformable because it is not fractional

Ahmed A. Abdelhakim

We point out a major flaw in the conformable calculus. We demonstrate why it fails at defining a fractional derivative and where exactly these tempting conformability properties co…

math.CA2018★ 8 cited

Precise interpretation of the conformable fractional derivative

Ahmed A. Abdelhakim

Let $α \in] 0, 1 [$ . We prove that the existence of the conformable fractional derivative $T_{α} f$ of a function $f : [0, \infty [⟶ R$ introduced by Khalil et al.…

math.CA2018★ 99 cited

A critical analysis of the conformable derivative

Ahmed A. Abdelhakim, José A. Tenreiro Machado

We prove that conformable ``fractional" differentiability of a function $f : [0, \infty [⟶ R$ is nothing else than the classical differentiability. More precis…

math.AP2018

On the boundary terms in Hardy's inequalities for $W^{1, p}$ functions

Ahmed A. Abdelhakim

With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for $W^{1, p}$ functions on bounded star domains. Our results a…

math.AP2017

Limiting case Hardy inequalities on the sphere

Ahmed A. Abdelhakim

We give sharp limiting case Hardy inequalities on the sphere $S^{2}$ and show that their optimal constants are unattainable by any $f\in H^{1}\left(\mathbb{S}^{2}\right)\s…

math.FA2017

A characterization of a nonlinear integral triangle inequality

Ahmed A. Abdelhakim

Let $(E, ∥.∥)$ be a Banach space and let $(Ω, μ)$ be a Lebesgue measure space. We characterize, for all $p > 0$ , measurable functions $u : Ω \to R$ for which \begin{equ…

math.FA2015

A convexity of functions on convex metric spaces of Takahashi and applications

Ahmed A. Abdelhakim

We quickly review and make some comments on the concept of convexity in metric spaces due to Takahashi. Then we introduce a concept of convex structure based convexity to functions…

math.AP2015

$L^{p}$ - $L^{q}$ boundedness of integral operators with oscillatory kernels: Linear versus quadratic phases

Ahmed A. Abdelhakim

Let $T_{N}^{j, k} : L^{p} (B) \to L^{q} ([0, 1])$ be the oscillatory integral operators defined by $\;\displaystyle T^{j,k}_{N}f(s):=\int_{B} \,f(x)\,e^{\imath N{|x|}^{j}s…

math.FA2015

On the summablility of truncated double Fourier series

Ahmed A. Abdelhakim

We estimate the truncated double trigonometric series $\sum_{n = 0}^{N} \sum_{m = 0}^{M} a_{mn} e^{2 π  (m x + n y)}$ , $a_{mn} \in C$ , in Lebesgue spaces with mixe…

A Littlewood-Paley approach to the Mittag-Leffler function in the frequency space and applications to nonlocal problems

On the asymptotic behaviour of the Fourier transform of the Mittag-Leffler function

Optimal critical exponent Lp inequalities of Hardy type on the sphere via Xiao's method

Sharp subcritical and critical Lp Hardy inequalities on the sphere

The flaw in the conformable calculus: it is conformable because it is not fractional

Precise interpretation of the conformable fractional derivative

A critical analysis of the conformable derivative

On the boundary terms in Hardy's inequalities for W1,p functions

Limiting case Hardy inequalities on the sphere

A characterization of a nonlinear integral triangle inequality

A convexity of functions on convex metric spaces of Takahashi and applications

Lp-Lq boundedness of integral operators with oscillatory kernels: Linear versus quadratic phases

On the summablility of truncated double Fourier series

Optimal critical exponent $L^{p}$ inequalities of Hardy type on the sphere via Xiao's method

Sharp subcritical and critical $L^{p}$ Hardy inequalities on the sphere

On the boundary terms in Hardy's inequalities for $W^{1, p}$ functions

$L^{p}$ - $L^{q}$ boundedness of integral operators with oscillatory kernels: Linear versus quadratic phases