Author
Ahmed M. A. El-Sayed
Other affiliations: Minia University
Bio: Ahmed M. A. El-Sayed is an academic researcher from Alexandria University. The author has contributed to research in topics: Fractional calculus & Differential equation. The author has an hindex of 30, co-authored 213 publications receiving 4495 citations. Previous affiliations of Ahmed M. A. El-Sayed include Minia University.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the stability of equilibrium points in the fractional-order predator-prey model and fractionalorder rabies model is studied and the existence and uniqueness of solutions are proved.
582 citations
TL;DR: In this paper, a new theory of thermoelasticity is derived using the methodology of fractional calculus, and a uniqueness theorem for this model is proved and a variational principle and a reciprocity theorem are derived.
445 citations
TL;DR: In this paper, some Routh-Hurwitz stability conditions are generalized to the fractional order case and the results agree with those obtained numerically for Lorenz, Rossler, Chua and Chen fractional-order equations.
375 citations
TL;DR: The stability, existence, uniqueness and numerical solution of the fractional-order logistic equation is studied here.
267 citations
TL;DR: The negative-direction fractional diffusion-wave problem was studied in this article, where the existence, uniqueness, and properties of the solution of the problem were established. But the authors did not consider the non-negative-direction version of the diffusion wave problem.
Abstract: The fractional-order diffusion-wave equation is an evolution equation of order α e (0, 2] which continues to the diffusion equation when α → 1 and to the wave equation when α → 2. We prove some properties of its solution and give some examples. We define a new fractional calculus (negative-direction fractional calculus) and study some of its properties. We study the existence, uniqueness, and properties of the solution of the negative-direction fractional diffusion-wave problem.
262 citations
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TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …
33,785 citations
Journal Article•
28,685 citations
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
7,412 citations
01 Jan 2015
3,828 citations