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

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5 papers · 1 filter

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.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…