Results 51 to 60 of about 39,478 (331)

The Variable-Order Fractional Calculus of Variations

, 2018
This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter 1) and of the
Almeida, Ricardo, Tavares, Dina, Torres, Delfim F. M.   +2 more
core   +1 more source

A new Definition of Fractional Derivative and Fractional Integral [PDF]

Kirkuk University Journal-Scientific Studies, 2018
In this paper, we introduce three different definitions of fractional derivatives, namely Riemann-Liouville derivative, Caputo derivative and the new formula Caputo expansion formula, and some basics properties of these derivatives are discussed.
openaire   +2 more sources

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 Operators, Dirichlet Averages, and Splines

, 2013
Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose of this paper
A. Kilbas, A. Pinkus, A. Shiryayev, A. Zemanian, B. Carlson, B. Carlson, B. Carlson, B. Carlson, B. Forster, B. Forster, B. Forster, B. Forster, B. Forster, B. Forster, B. Forster, C. Micchelli, D. Baleanu, E. Hille, E. Neuman, G. Anastassiou, I. Podlubny, M. Ortigueira, M. Troyanov, M. Unser, M. Unser, P. Butzer, P. Massopust, P. Massopust, P. Massopust, R. Dantry, R. Hilfer, S. Karlin, S. Samko, S. Samko, S.F. Karlin, U. Westphal, V. Zheludev, W. Dahmen   +37 more
core   +1 more source

Diffusive representations for fractional Laplacian: systems theory framework and numerical issues [PDF]

, 2009
Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not ...
Matignon, Denis
core   +1 more source

Calculus of variations with fractional derivatives and fractional integrals

Applied Mathematics Letters, 2009
We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.
Almeida, R., Torres, D.F.M.
openaire   +4 more sources

Real‐time assay of ribonucleotide reductase activity with a fluorescent RNA aptamer

FEBS Letters, EarlyView.
Ribonucleotide reductases (RNR) synthesize DNA building blocks de novo, making them crucial in DNA replication and drug targeting. FLARE introduces the first single‐tube real‐time coupled RNR assay, which enables isothermal tracking of RNR activity at nanomolar enzyme levels and allows the reconstruction of allosteric regulatory patterns and rapid ...
Jacopo De Capitani, Noemi E. Nwosu, Viktoria Gocke, Müge Kasanmascheff, Hannes Mutschler   +4 more
wiley   +1 more source

Fractional Calculus: Theory and Applications

Mathematics, 2018
Fractional calculus is allowing integrals and derivatives of any positive order (the term fractional is kept only for historical reasons).[...]
Francesco Mainardi
doaj   +1 more source

Modified Optimal Energy and Initial Memory of Fractional Continuous-Time Linear Systems

, 2010
Fractional systems with Riemann-Liouville derivatives are considered. The initial memory value problem is posed and studied. We obtain explicit steering laws with respect to the values of the fractional integrals of the state variables.
Mozyrska, Dorota, Torres, Delfim F. M.
core   +1 more source

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