Results 41 to 50 of about 59,224 (329)

Concavity in fractional calculus

Filomat, 2018
We discuss a concavity like property for functions u satisfying D?0+u ? C[0, b] with u(0) = 0 and -D?0+u(t) ? 0 for all t ? [0,b]. We develop the property for ? ? (1,2], where D?0+ is the standard Riemann-Liouville fractional derivative. We observe the property is also valid in the case ? = 1. Finally, we show that under certain conditions,
Eloe, Paul W., Neugebauer, Jeffrey T.
openaire   +2 more sources

On Implicit Atangana–Baleanu–Caputo Fractional Integro-Differential Equations with Delay and Impulses

Journal of Mathematics
In this paper, we study the existence and uniqueness of solutions for impulsive Atangana-Baleanu-Caputo ABC fractional integro-differential equations with boundary conditions.
Panjaiyan Karthikeyann, Sadhasivam Poornima, Kulandhaivel Karthikeyan, Chanon Promsakon, Thanin Sitthiwirattham   +4 more
doaj   +1 more source

Implementation of fractional order integrator/differentiator on field programmable gate array

Alexandria Engineering Journal, 2016
Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus ...
K.P.S. Rana, V. Kumar, N. Mittra, N. Pramanik   +3 more
doaj   +1 more source

Holder exponents of irregular signals and local fractional derivatives

, 1997
It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations.
A Arneodo, A B Chhabra, A Juneja, A Ott, A S Besicovitch, A Zygmund, Anil D Gangal, B B Mandelbrot, B B Mandelbrot, B B Mandelbrot, B Ross, C Meneveau, E M Stein, E M Stein, G H Hardy, G H Hardy, G Jumarie, G M Zaslavsky, G V Welland, H C Fogedby, H E Roman, I Daubechies, I Eyink, J D Farmer, J F Muzy, J Feder, J Gerver, J J Duistermaat, J L Kaplan, J P Bouchaud, K B Oldham, K Falconer, K L Sebastian, K M Kolwankar, K S Miller, K Sarkar, Kiran M Kolwankar, L F Abott, M F Schlesinger, M F Shlesinger, M F Shlesinger, M F Shlesinger, M Giona, M H Jensen, M Holschneider, M Holschneider, M V Berry, M Zähle, N Patzschke, P Collet, P Constantin, P Constantin, R Benzi, R Benzi, R Cawley, R D Mauldin, R Hilfer, R Hilfer, R P Feynmann, R Riedi, S Jaffard, T C Halsey, T H Solomon, T J Osler, T Vicsek, T W Körner, U Frisch, W G Glöckle, W R Schneider, W Wyss   +69 more
core   +2 more sources

Fractional calculus for distributions

Fractional Calculus and Applied Analysis
AbstractFractional derivatives and integrals for measures and distributions are reviewed. The focus is on domains and co-domains for translation invariant fractional operators. Fractional derivatives and integrals interpreted as "Equation missing"-convolution operators with power law kernels are found to have the largest domains of definition.
Hilfer, Rudolf, Kleiner, Tillmann
openaire   +3 more sources

Aβ42 promotes the aggregation of α‐synuclein splice isoforms via heterogeneous nucleation

FEBS Letters, EarlyView.
The aggregation of amyloid‐β (Aβ) and α‐synuclein (αSyn) is associated with Alzheimer's and Parkinson's diseases. This study reveals that Aβ aggregates serve as potent nucleation sites for the aggregation of αSyn and its splice isoforms, shedding light on the intricate interplay between these two pathogenic proteins.
Alexander Röntgen, Zenon Toprakcioglu, Michele Vendruscolo   +2 more
wiley   +1 more source

Fractional Order Sequential Minimal Optimization Classification Method

Fractal and Fractional, 2023
Sequential minimal optimization (SMO) method is an algorithm for solving optimization problems arising from the training process of support vector machines (SVM).
Chunna Zhao, Licai Dai, Yaqun Huang
doaj   +1 more source

Coupled systems of fractional equations related to sound propagation: analysis and discussion [PDF]

, 2012
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in the ...
Diethelm K., Federico Polito, Fellah Z. E. A., Haubold H. J., Kilbas A. A., Podlubny I., Roberto Garra   +6 more
core   +1 more source

Marvels of fractional calculus

Tbilisi Mathematical Journal, 2017
This is an expository article that describes, in brief, one of the preeminent branch of applicable mathematics, roots of which lie in the nucleus of pure mathematics that ruled the research since past six decades. In writing this article though several important research papers were excised yet attempt is made to retain the beauty of fractional ...
Banerji, P. K., Loonker, Deshna
openaire   +3 more sources

Redox‐dependent binding and conformational equilibria govern the fluorescence decay of NAD(P)H in living cells

FEBS Letters, EarlyView.
In this work, we reveal how different enzyme binding configurations influence the fluorescence decay of NAD(P)H in live cells using time‐resolved anisotropy imaging and fluorescence lifetime imaging microscopy (FLIM). Mathematical modelling shows that the redox states of the NAD and NADP pools govern these configurations, shaping their fluorescence ...
Thomas S. Blacker, Nimit Mistry, Nicoletta Plotegher, Elizabeth R. Westbrook, Michael D. E. Sewell, John Carroll, Gyorgy Szabadkai, Angus J. Bain, Michael R. Duchen   +8 more
wiley   +1 more source