A. A. Abdelhakim

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20152020

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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

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.…