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1

Matrix approach to discrete fractional calculus II: Partial fractional differential equations

Igor Podlubny, Aleksei Chechkin, Tomas Skovranek, YangQuan Chen, Blas M. Vinagre Jara

Journal:

Journal of Computational Physics

Year:

2009

Language:

english

File:

PDF, 2.78 MB

english, 2009

2

From continuous time random walks to the generalized diffusion equation

Sandev, Trifce, Metzler, Ralf, Chechkin, Aleksei

Journal:

Fractional Calculus and Applied Analysis

Year:

2018

Language:

english

File:

PDF, 410 KB

english, 2018

3

Bulk-mediated surface diffusion along a cylinder: Propagators and crossovers

Chechkin, Aleksei V., Zaid, Irwin M., Lomholt, Michael A., Sokolov, Igor M., Metzler, Ralf

Journal:

Physical Review E

Year:

2009

Language:

english

File:

PDF, 109 KB

english, 2009

4

Continuous-time random walk with correlated waiting times

Chechkin, Aleksei V., Hofmann, Michael, Sokolov, Igor M.

Journal:

Physical Review E

Year:

2009

Language:

english

File:

PDF, 170 KB

english, 2009

5

Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion

Jeon, Jae-Hyung, Chechkin, Aleksei V., Metzler, Ralf

Journal:

Physical Chemistry Chemical Physics

Year:

2014

Language:

english

File:

PDF, 2.04 MB

english, 2014

6

Generalized Elastic Model Yields a Fractional Langevin Equation Description

Taloni, Alessandro, Chechkin, Aleksei, Klafter, Joseph

Journal:

Physical Review Letters

Year:

2010

Language:

english

File:

PDF, 191 KB

english, 2010

7

Bulk-mediated diffusion on a planar surface: Full solution

Chechkin, Aleksei V., Zaid, Irwin M., Lomholt, Michael A., Sokolov, Igor M., Metzler, Ralf

Journal:

Physical Review E

Year:

2012

Language:

english

File:

PDF, 210 KB

english, 2012

8

Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes

Cherstvy, Andrey G, Chechkin, Aleksei V, Metzler, Ralf

Journal:

New Journal of Physics

Year:

2013

Language:

english

File:

PDF, 651 KB

english, 2013

9

Correlated continuous time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics

Schulz, Johannes H P, Chechkin, Aleksei V, Metzler, Ralf

Journal:

Journal of Physics A Mathematical and Theoretical

Year:

2013

Language:

english

File:

PDF, 480 KB

english, 2013

10

Aging scaled Brownian motion

Safdari, Hadiseh, Chechkin, Aleksei V., Jafari, Gholamreza R., Metzler, Ralf

Journal:

Physical Review E

Year:

2015

Language:

english

File:

PDF, 5.92 MB

english, 2015

11

Brownian yet Non-Gaussian Diffusion: From Superstatistics to Subordination of Diffusing Diffusivities

Chechkin, Aleksei V., Seno, Flavio, Metzler, Ralf, Sokolov, Igor M.

Journal:

Physical Review X

Year:

2017

Language:

english

File:

PDF, 550 KB

english, 2017

12

Fluctuations of random walks in critical random environments

Mardoukhi, Yousof, Jeon, Jae-Hyung, Chechkin, Aleksei V., Metzler, Ralf

Journal:

Physical Chemistry Chemical Physics

Year:

2018

Language:

english

File:

PDF, 2.11 MB

english, 2018

13

Time averages and their statistical variation for the Ornstein-Uhlenbeck process: Role of initial particle distributions and relaxation to stationarity

Cherstvy, Andrey G., Thapa, Samudrajit, Mardoukhi, Yousof, Chechkin, Aleksei V., Metzler, Ralf

Journal:

Physical Review E

Year:

2018

Language:

english

File:

PDF, 948 KB

english, 2018

14

Some fundamental aspects of Lévy flights

Ralf Metzler, Aleksei V. Chechkin, Vsevolod Yu. Gonchar, Joseph Klafter

Journal:

Chaos, Solitons & Fractals

Year:

2007

Language:

english

File:

PDF, 294 KB

english, 2007

15

Relaxation to stationary states for anomalous diffusion

Bartłomiej Dybiec, Igor M. Sokolov, Aleksei V. Chechkin

Journal:

Communications in Nonlinear Science and Numerical Simulation

Year:

2011

Language:

english

File:

PDF, 438 KB

english, 2011

16

Lévy Flights in a Steep Potential Well

Aleksei V. Chechkin, Vsevolod Yu. Gonchar, Joseph Klafter, Ralf Metzler, Leonid V. Tanatarov

Journal:

Journal of Statistical Physics

Year:

2004

Language:

english

File:

PDF, 1012 KB

english, 2004

17

Unusual response to a localized perturbation in a generalized elastic model

Taloni, Alessandro, Chechkin, Aleksei, Klafter, Joseph

Journal:

Physical Review E

Year:

2011

Language:

english

File:

PDF, 392 KB

english, 2011

18

Correlations in a generalized elastic model: Fractional Langevin equation approach

Taloni, Alessandro, Chechkin, Aleksei, Klafter, Joseph

Journal:

Physical Review E

Year:

2010

Language:

english

File:

PDF, 260 KB

english, 2010

19

Stationary states in single-well potentials under symmetric Lévy noises

Dybiec, Bartłomiej, Sokolov, Igor M, Chechkin, Aleksei V

Journal:

Journal of Statistical Mechanics Theory and Experiment

Year:

2010

Language:

english

File:

PDF, 1.15 MB

english, 2010

20

First passage and arrival time densities for Lévy flights and the failure of the method of images

Chechkin, Aleksei V, Metzler, Ralf, Gonchar, Vsevolod Y, Klafter, Joseph, Tanatarov, Leonid V

Journal:

Journal of Physics A: Mathematical and General Physics

Year:

2003

Language:

english

File:

PDF, 198 KB

english, 2003

21

Diffusion in randomly perturbed dissipative dynamics

Rodrigues, Christian S., Chechkin, Aleksei V., de Moura, Alessandro P. S., Grebogi, Celso, Klages, Rainer

Journal:

EPL (Europhysics Letters)

Year:

2014

Language:

english

File:

PDF, 434 KB

english, 2014

22

Kramers-like escape driven by fractional Gaussian noise

Sliusarenko, Oleksii Yu., Gonchar, Vsevolod Yu., Chechkin, Aleksei V., Sokolov, Igor M., Metzler, Ralf

Journal:

Physical Review E

Year:

2010

Language:

english

File:

PDF, 373 KB

english, 2010

23

Bifurcation, bimodality, and finite variance in confined Lévy flights

Chechkin, Aleksei V., Klafter, Joseph, Gonchar, Vsevolod Yu., Metzler, Ralf, Tanatarov, Leonid V.

Journal:

Physical Review E

Year:

2003

Language:

english

File:

PDF, 65 KB

english, 2003

24

Natural cutoff in Lévy flights caused by dissipative nonlinearity

Chechkin, Aleksei V., Gonchar, Vsevolod Yu., Klafter, Joseph, Metzler, Ralf

Journal:

Physical Review E

Year:

2005

Language:

english

File:

PDF, 266 KB

english, 2005

25

Fractal properties of anomalous diffusion in intermittent maps

Korabel, Nickolay, Klages, Rainer, Chechkin, Aleksei V., Sokolov, Igor M., Gonchar, Vsevolod Yu.

Journal:

Physical Review E

Year:

2007

Language:

english

File:

PDF, 546 KB

english, 2007

26

Spatiotemporal Dynamics of Bumblebees Foraging under Predation Risk

Lenz, Friedrich, Ings, Thomas C., Chittka, Lars, Chechkin, Aleksei V., Klages, Rainer

Journal:

Physical Review Letters

Year:

2012

Language:

english

File:

PDF, 467 KB

english, 2012

27

Codifference as a practical tool to measure interdependence

Wyłomańska, Agnieszka, Chechkin, Aleksei, Gajda, Janusz, Sokolov, Igor M.

Journal:

Physica A: Statistical Mechanics and its Applications

Year:

2015

Language:

english

File:

PDF, 933 KB

english, 2015

28

close to 2

Burnecki, Krzysztof, Wyłomańska, Agnieszka, Beletskii, Aleksei, Gonchar, Vsevolod, Chechkin, Aleksei

Journal:

Physical Review E

Year:

2012

Language:

english

File:

PDF, 2.32 MB

english, 2012

29

Leapover Lengths and First Passage Time Statistics for Lévy Flights

Koren, Tal, Lomholt, Michael A., Chechkin, Aleksei V., Klafter, Joseph, Metzler, Ralf

Journal:

Physical Review Letters

Year:

2007

Language:

english

File:

PDF, 301 KB

english, 2007

30

Barrier crossing driven by Lévy noise: Universality and the role of noise intensity

Chechkin, Aleksei V., Sliusarenko, Oleksii Yu., Metzler, Ralf, Klafter, Joseph

Journal:

Physical Review E

Year:

2007

Language:

english

File:

PDF, 686 KB

english, 2007

31

Ageing and confinement in non-ergodic heterogeneous diffusion processes

Cherstvy, Andrey G, Chechkin, Aleksei V, Metzler, Ralf

Journal:

Journal of Physics A Mathematical and Theoretical

Year:

2014

Language:

english

File:

PDF, 158 KB

english, 2014

32

Localisation and universal fluctuations in ultraslow diffusion processes

Godec, Aljaž, Chechkin, Aleksei V, Barkai, Eli, Kantz, Holger, Metzler, Ralf

Journal:

Journal of Physics A Mathematical and Theoretical

Year:

2014

Language:

english

File:

PDF, 2.34 MB

english, 2014

33

Diffusion and Fokker-Planck-Smoluchowski Equations with Generalized Memory Kernel

Sandev, Trifce, Chechkin, Aleksei, Kantz, Holger, Metzler, Ralf

Journal:

Fractional Calculus and Applied Analysis

Year:

2015

Language:

english

File:

PDF, 434 KB

english, 2015

34

Effective surface motion on a reactive cylinder of particles that perform intermittent bulk diffusion

Chechkin, Aleksei V., Zaid, Irwin M., Lomholt, Michael A., Sokolov, Igor M., Metzler, Ralf

Journal:

The Journal of Chemical Physics

Year:

2011

Language:

english

File:

PDF, 445 KB

english, 2011

35

Quantifying non-ergodic dynamics of force-free granular gases

Bodrova, Anna, Chechkin, Aleksei V., Cherstvy, Andrey G., Metzler, Ralf

Journal:

Physical Chemistry Chemical Physics

Year:

2015

Language:

english

File:

PDF, 2.12 MB

english, 2015

36

Quantifying the non-ergodicity of scaled Brownian motion

Safdari, Hadiseh, Cherstvy, Andrey G, Chechkin, Aleksei V, Thiel, Felix, Sokolov, Igor M, Metzler, Ralf

Journal:

Journal of Physics A Mathematical and Theoretical

Year:

2015

Language:

english

File:

PDF, 2.32 MB

english, 2015

37

Directed transport induced by spatially modulated Lévy flights

Pavlyukevich, Ilya, Li, Yongge, Xu, Yong, Chechkin, Aleksei

Journal:

Journal of Physics A Mathematical and Theoretical

Year:

2015

Language:

english

File:

PDF, 638 KB

english, 2015

38

Distributed-order diffusion equations and multifractality: Models and solutions

Sandev, Trifce, Chechkin, Aleksei V., Korabel, Nickolay, Kantz, Holger, Sokolov, Igor M., Metzler, Ralf

Journal:

Physical Review E

Year:

2015

Language:

english

File:

PDF, 815 KB

english, 2015

39

A model of return intervals between earthquake events

Zhou, Yu, Chechkin, Aleksei, Sokolov, Igor M., Kantz, Holger

Journal:

EPL (Europhysics Letters)

Year:

2016

Language:

english

File:

PDF, 328 KB

english, 2016

40

Search reliability and search efficiency of combined Lévy–Brownian motion: long relocations mingled with thorough local exploration

Palyulin, Vladimir V, Chechkin, Aleksei V, Klages, Rainer, Metzler, Ralf

Journal:

Journal of Physics A Mathematical and Theoretical

Year:

2016

Language:

english

File:

PDF, 812 KB

english, 2016

41

Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion

Bodrova, Anna S., Chechkin, Aleksei V., Cherstvy, Andrey G., Safdari, Hadiseh, Sokolov, Igor M., Metzler, Ralf

Journal:

Scientific Reports

Year:

2016

Language:

english

File:

PDF, 928 KB

english, 2016

42

Space-fractional Fokker–Planck equation and optimization of random search processes in the presence of an external bias

Palyulin, Vladimir V, Chechkin, Aleksei V, Metzler, Ralf

Journal:

Journal of Statistical Mechanics Theory and Experiment

Year:

2014

Language:

english

File:

PDF, 1.12 MB

english, 2014

43

To hit or to pass it over—remarkable transient behavior of first arrivals and passages for Lévy flights in finite domains

Dybiec, Bartłomiej, Gudowska-Nowak, Ewa, Chechkin, Aleksei

Journal:

Journal of Physics A Mathematical and Theoretical

Year:

2016

Language:

english

File:

PDF, 994 KB

english, 2016

44

Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation

Safdari, Hadiseh, Cherstvy, Andrey G., Chechkin, Aleksei V., Bodrova, Anna, Metzler, Ralf

Journal:

Physical Review E

Year:

2017

Language:

english

File:

PDF, 1.98 MB

english, 2017

45

Beyond monofractional kinetics

Sandev, Trifce, Sokolov, Igor M., Metzler, Ralf, Chechkin, Aleksei

Journal:

Chaos, Solitons & Fractals

Year:

2017

Language:

english

File:

PDF, 529 KB

english, 2017

46

Comparison of pure and combined search strategies for single and multiple targets

Palyulin, Vladimir V., Mantsevich, Vladimir N., Klages, Rainer, Metzler, Ralf, Chechkin, Aleksei V.

Journal:

The European Physical Journal B / Condensed Matter and Complex Systems

Year:

2017

Language:

english

File:

PDF, 646 KB

english, 2017

47

Ageing effects in ultraslow continuous time random walks

Chechkin, Aleksei V., Kantz, Holger, Metzler, Ralf

Journal:

The European Physical Journal B / Condensed Matter and Complex Systems

Year:

2017

Language:

english

File:

PDF, 497 KB

english, 2017

48

Bacterial bioluminescence onset and quenching: a dynamical model for a quorum sensing -mediated property

Side, Domenico Delle, Nassisi, Vincenzo, Pennetta, Cecilia, Alifano, Pietro, Di Salvo, Marco, Talà, Adelfia, Chechkin, Aleksei, Seno, Flavio, Trovato, Antonio

Journal:

Royal Society Open Science

Year:

2017

Language:

english

File:

PDF, 747 KB

english, 2017

49

Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem

Burnecki, Krzysztof, Wylomanska, Agnieszka, Chechkin, Aleksei, Chen, Zhongxue

Journal:

Year:

2015

Language:

english

File:

PDF, 490 KB

english, 2015

50

Conservative random walks in confining potentials

Dybiec, Bartlomiej, Capała, Karol Piotr, Chechkin, Aleksei V, Metzler, Ralf

Journal:

Journal of Physics A Mathematical and Theoretical

Year:

2018

Language:

english

File:

PDF, 3.97 MB

english, 2018