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Foundations, Volume 2, Issue 3

September 2022 - 21 articles

Cover Story: Λ-fractional analysis has been introduced solely to fill the mathematical gap exhibited in fractional calculus, where the various fractional derivatives fail to fulfill the prerequisites demanded by differential topology. Nevertheless, the various advantages exhibited by the fractional derivatives, and especially their non-local character, attracted the interest of physicists, although the majority of them try to avoid them. The introduced Λ-fractional analysis can generate fractional geometry since the Λ-fractional derivatives generate differentials. The Λ-fractional analysis has been introduced to science to formulate non-local response problems with the demanded mathematical accuracy. View this paper
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Articles (21)

  • Review
  • Open Access
3 Citations
4,015 Views
17 Pages

17 August 2022

From the perspectives of the thermodynamics of irreversible processes and the theory of complex systems, a characterization of longevity and aging and their relationships with the emergence and evolution of cancer was carried out. It was found that:...

  • Article
  • Open Access
3 Citations
6,208 Views
25 Pages

5 August 2022

The ground-based monitoring of the lower ionosphere by studying the perturbations of the subionospheric propagation of very-low-frequency/low-frequency (VLF/LF) signals is important in the research of a wide variety of geophysical and Sun/space extre...

  • Article
  • Open Access
1,586 Views
7 Pages

Approximating Solutions of Nonlinear Equations Using an Extended Traub Method

  • Santhosh George,
  • Ioannis K. Argyros,
  • Christopher I. Argyros and
  • Kedarnath Senapati

The Traub iterates generate a sequence that converges to a solution of a nonlinear equation given certain conditions. The order of convergence has been shown provided that the fifth Fréchet-derivative exists. Notice that this derivative does n...

  • Article
  • Open Access
2 Citations
1,984 Views
10 Pages

In this paper, we give new Simpson’s type integral inequalities for the class of functions whose derivatives of absolute values are s-convex via generalized proportional fractional integrals. Some results in the literature are particular cases...

  • Article
  • Open Access
5 Citations
2,136 Views
17 Pages

Attenuation of the Acoustic Activity in Cement Beams under Constant Bending Load Closely Approaching the Fracture Load

  • Dimos Triantis,
  • Andronikos Loukidis,
  • Ilias Stavrakas,
  • Ermioni D. Pasiou and
  • Stavros K. Kourkoulis

The acoustic activity in beam-shaped specimens made of cement is studied, assuming that the beams are loaded in three-point bending under a step-wise loading scheme. Attention is focused to the attenuation of the acoustic activity during the constant...

  • Article
  • Open Access
2,365 Views
9 Pages

In the first part of this paper, we considered several theoretical models, a static and four dynamic models without rebounds, of the throw of a fair coin landing on its edge, to demonstrate that the probability of heads or tails is less than 50%, dep...

  • Article
  • Open Access
3 Citations
2,956 Views
20 Pages

Electromagnetic radiation (EMR) technology makes it possible to evaluate changes in the stress-strain state (SSS) in the “tunnel lining-enclosing rock mass” system at a high level of interference, and to create schemes of long-term EMR co...

  • Article
  • Open Access
1 Citations
2,931 Views
14 Pages

Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails of less than 50%. In this first part, the theoretical models for a static case...

  • Communication
  • Open Access
11 Citations
2,294 Views
6 Pages

For the excitation of the n = 2 states of hydrogen atoms due to electron impact, we compared the experimental and theoretical ratios of the cross-sections σ2s/σ2p. We found this theoretical ratio to be systematically higher than the corre...

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Foundations - ISSN 2673-9321