Results 41 to 50 of about 74,438 (274)
Distributed Order Derivatives and Relaxation Patterns
, 2009 We consider equations of the form $(D_{(\rho)}u)(t)=-\lambda u(t)$, $t>0$, where $\lambda >0$, $D_{(\rho)}$ is a distributed order derivative, that is the Caputo-Dzhrbashyan fractional derivative of order $\alpha$, integrated in $\alpha\in (0,1)$ with ...
Anatoly N Kochubei +12 more
core +1 more source
Hydrology, 2017 This paper presents solutions of the fractional partial differential equation (fPDE) for analysing water movement in soils. The fPDE explains processes equivalent to the concept of symmetrical fractional derivatives (SFDs) which have two components: the ...
Ninghu Su
doaj +1 more source
Time-fractional diffusion of distributed order
, 2007 The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense.
Gorenflo, Rudolf +3 more
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Diffusion with space memory modelled with distributed order space fractional differential equations
Annals of Geophysics, 2003 Distributed order fractional differential equations (Caputo, 1995, 2001; Bagley and Torvik, 2000a,b) were fi rst used in the time domain; they are here considered in the space domain and introduced in the constitutive equation of diffusion.
M. Caputo
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The two forms of fractional relaxation of distributed order
, 2006 The first-order differential equation of exponential relaxation can be generalized by using either the fractional derivative in the Riemann-Liouville (R-L) sense and in the Caputo (C) sense, both of a single order less than 1.
Gorenflo, Rudolf +3 more
core +3 more sources
, 2009 System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense.
Atanackovic, Teodor M. +2 more
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Molecular bases of circadian magnesium rhythms across eukaryotes
FEBS Letters, EarlyView.Circadian rhythms in intracellular [Mg2+] exist across eukaryotic kingdoms. Central roles for Mg2+ in metabolism suggest that Mg2+ rhythms could regulate daily cellular energy and metabolism. In this Perspective paper, we propose that ancestral prokaryotic transport proteins could be responsible for mediating Mg2+ rhythms and posit a feedback model ...
Helen K. Feord, Gerben van Ooijen
wiley +1 more source
Fractional Langevin Equation of Distributed Order
, 2010 Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent.
Eab, C. H., Lim, S. C.
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Disordered but rhythmic—the role of intrinsic protein disorder in eukaryotic circadian timing
FEBS Letters, EarlyView.Unstructured domains known as intrinsically disordered regions (IDRs) are present in nearly every part of the eukaryotic core circadian oscillator. IDRs enable many diverse inter‐ and intramolecular interactions that support clock function. IDR conformations are highly tunable by post‐translational modifications and environmental conditions, which ...
Emery T. Usher, Jacqueline F. Pelham
wiley +1 more source
Fractal and Fractional, 2023 A comb structure consists of a one-dimensional backbone with lateral branches. These structures have widespread application in medicine and biology. Such a structure promotes an anomalous diffusion process along the backbone (x-direction), along with ...
Lin Liu +7 more
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