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A Survey of Numerical Methods in Fractional Calculus. Fractional Derivatives in Mechanics: State of the Art. CNAM Paris, 17 November 2006. Kai Diethelm ...

http://www.cnam.fr/lmssc/seminaires/derivfrac/diethelm/VORTRAG.PDF

by R GORENFLO - Cited by 61

http://www.fracalmo.org/download/rgcism10.pdf

by K Diethelm - 2005 - Cited by 67

http://www.tfh-berlin.de/~luchko/papers/FreedFordDiethelmLuchko.pdf

our numerical methods for problems described by fractional-order ... A survey of many emerging applications of the fractional calculus in areas of science ...

http://141.64.226.10/~luchko/papers/FreedFordDiethelmLuchko.pdf

by M Stojanovic - Related articles

http://anotrans.physik.hu-berlin.de/abstracts/stojanovic_abs.pdf

File Format: PDF/Adobe Acrobatby AJ Landy - 2009Fractional Calculus is the evaluation of derivatives and integrals, where the order of the ... Develop equations of existing numerical methods for their solution, ... It is not a comprehensive survey of all papers, ...

http://chesterrep.openrepository.com/cdr/bitstream/10034/93746/2/chapter 1.pdf

File Format: PDF/Adobe Acrobatby JA Connolly - 2004To enhance an engineer's ability to use fractional calculus as a modelling ... This technique is used to compare numerical methods for single- ... A brief survey of the possible uses of fractional differential equations is presented. ...

http://chesterrep.openrepository.com/cdr/bitstream/10034/76687/2/chapter 1.pdf

Other Methods for the Solution of. Fractional-order Equations ... calculus. Numerical solution of nonlinear problems. 9. Survey of Applications ...

http://people.tuke.sk/igor.podlubny/USU/01_name.pdf

by K Diethelm - Cited by 32

http://www.billingpreis.mpg.de/hbp98/diethelm.pdf

Thirdly, we conclude the paper with a survey of the required theory. ... becomes evident by comparing the numerical results with measurement. ...... Kempfle, S. and Schäfer, I., 'Functional calculus method versus Riemann–Liouville ...

http://www.springerlink.com/index/W023VGPNCW4X7E9M.pdf

In this paper, extension of fractional calculus models to the non-linear range ... oped for at least the past half century [1–5] (see the historical survey of .... or in the presence of non-linear viscoelasticity, a numerical solution is .... Two methods of integration have been used. One is based on the Grünwald ...

http://www.springerlink.com/index/W3625T7J0236W141.pdf

by M Lia - Cited by 1

http://www.cc.ac.cn/2009research_report/0903.pdf

first section below provides a brief review of fractional calculus. ... An outstanding historical survey can be found in [27] who also give what is ..... [28] R. Piche, "Noise-filtering properties of numerical methods for the ...

http://www.eecs.berkeley.edu/~chua/papers/Hartley95.pdf

by H Farid - Related articles

http://www.cs.dartmouth.edu/farid/publications/tr04b.pdf

by G Cooper - 2003 - Cited by 17

http://web.wits.ac.za/NR/rdonlyres/1B70EBC2-BF77-4577-A0EA-FD68FA268FA6/0/2003Fractional.pdf

by C Lubich - 1985 - Cited by 71

http://www.sam.math.ethz.ch/~hiptmair/Seminars/CONVQUAD/Articles/LUB85.pdf

Prerequisites : Knowledge of calculus and numerical methods as acquired during the first two ... Numerical inversion of the Laplace transform: A survey ...

http://www.sam.math.ethz.ch/~hiptmair/Seminars/CONVQUAD/fastnumericalconvolution.pdf

Generally, the numerical methods such as Runge Kutta method are based on the ..... fractional calculus including extensive survey on fractional differential ...

http://www.jadavpur.edu/conference/INTRODUCTION_Ssaharoy.pdf

by F Mainardi - Related articles

http://downloads.hindawi.com/journals/ijde/2010/104505.pdf

by F Merrikh-Bayat - 2008 - Cited by 3

http://downloads.hindawi.com/journals/jam/2008/528934.pdf

by CC Tseng - 2001 - Cited by 47

http://mechatronics.ece.usu.edu/foc/FRFT/references/x00905945Design of fractional order digital FIR differentiators.pdf

by T Bhaskaran - Cited by 7

http://mechatronics.ece.usu.edu/foc/event/FOC_Day@USU/2007_files/DETC2007-34302fopi1.pdf

by S Shaw - 1998 - Cited by 6

http://dml.cz/bitstream/handle/10338.dmlcz/700266/Equadiff_09-1997-1_13.pdf

We investigate the stability properties of numerical methods for weakly singular ..... BRUNNER, H. 1982 A survey of recent advances in the numerical treatment ... 1985a Discretized fractional calculus. SLAM J. math. Anal, (to appear). ...

http://imajna.oxfordjournals.org/cgi/reprint/6/1/87.pdf

by KAI DIETTELM - 1997 - Cited by 14

http://imajna.oxfordjournals.org/cgi/reprint/17/3/479.pdf

by A Ghorbani - Cited by 1

http://www.emis.de/journals/HOA/MPE/Volume2008/627983.pdf

In [9, 34] fractional calculus is mathematically based on corresponding integral and ... Ruschisky gave survey of both structure and analysis of the rheological models of ...... and numerical methods for exploring these structures and ...

http://www.emis.de/journals/HOA/MPE/Volume2006/n1_13.pdf

A generalized fractional calculus and integral transforms (Kiryakova V. S.). Proc. Conf. .... Transmutation methods for solving Erdelyi-Kober fractional differintegal ... Numerical Functional Analysis and Optimization, 2000, 21, No 1-2,. 121-144. .... Survey Brochure. = Обзор под формата на ...

http://www.math.bas.bg/new/site/images/pub_7bc930006bd10e20272deab57cb8b975.pdf

OPERATIONAL METHOD IN FRACTIONAL CALCULUS . . . . . . . . .463. S.T. Mincheva ..... NUMERICAL SOLUTION METHODS FOR. DISTRIBUTED ORDER DIFFERENTIAL EQUATIONS .......... 531. Yu.A. Brychkov ...... A TUTORIAL SURVEY . ...

http://www.math.bas.bg/~fcaa/contfc_all_10vol.pdf

by A KILBAS - Cited by 440

http://www.gbv.de/dms/goettingen/501829326.pdf

2 Nov 2009 ... A Seminar on Fractional Calculus in BioEngineering ... Numerical and Analytical Solutions of Fractional Differential Equations, ... SURVEY;. - R. Hilfer, Y. Luchko, Z. Tomovski, OPERATIONAL METHOD FOR THE SOLUTION OF ...

http://www.ims-bordeaux.eu/IMS/ressources/fichiers/NGFlMDUzODViNDY3Nw==/NewsletterIFAC3.pdf

by M Burger - Cited by 75

ftp://ftp.math.ucla.edu/pub/camreport/cam04-02.pdf

by YQ Chen - 2009 - Related articles

http://www.nt.ntnu.no/users/skoge/prost/proceedings/acc09/data/papers/1371.pdf

by V Bhambhani - Cited by 6

http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2008/data/papers/2598.pdf

of fractional calculus build the fundament of any numerical methods for differential ... One important aspect in Chapter 5 is a careful survey of the possi- ...

http://bib1lp1.rz.tu-bs.de/docportal/servlets/MCRFileNodeServlet/DocPortal_derivate_00002234/dissertation.pdf?hosts=local

First a survey is presented on how space-time fractional diffusion processes ... In recent years methods of fractional calculus have met more and more interest and ...... [17] K, Diethelm and N.J. Ford, Numerical solution methods for ...

http://iopscience.iop.org/1742-6596/7/1/001/pdf/1742-6596_7_1_001.pdf

Even more recently, a discrete-time fractional calculus has been developed similar to the theory of linear multistep methods for numerical integration ...

http://ieeexplore.ieee.org/iel4/81/9087/00404062.pdf

Various PID tuning methods for temperature control have been developed by the many industries.4 For the reliable ... From a literature survey, it is shown that there have been .... α using numerical classical approach in MATLAB. Once .... [15] J. A. Tenreiro Machado, “Special Issue on Fractional Calculus and ...

http://ieeexplore.ieee.org/iel5/4588287/4597261/04598234.pdf?arnumber=4598234

by HYOS AHN - 2009 - Related articles

http://www.ias.ac.in/sadhana/Pdf2009Oct/833.pdf

by F Saedpanah - Related articles

http://www.math.chalmers.se/Math/Research/Preprints/2007/37.pdf

This concept is based on the theory of fractional calculus. .... In this work a survey of FDP and FD models is attempted and corresponding example ...... In considering numerical methods to solve integro-differential equations, it is es ...

http://scholarship.rice.edu/bitstream/handle/1911/17148/1389059.PDF?sequence=1

hensive survey of Brass and Forster [1] that contains many further results about ..... Appendix Some results from fractional calculus ... [7] P. Linz, Analytical and Numerical Methods for Volterra Equations, SIAM, Philadelphia, 1985. ...

http://www.informaworld.com/index/777140535.pdf

the numerical tests: • The fractional BDF method of order 3 to the power 1/2 is chosen. .... A survey of regularization methods for first-kind Volterra equations. ... Discretized fractional calculus. SIAM J. Math. Anal. 17(3):704–719. ...

http://www.informaworld.com/index/K01556N24188K66X.pdf

by VS Erturk - 2007 - Cited by 8

http://qspace.qu.edu.qa/bitstream/handle/10576/10524/Application of generalized differential transform method to multi-order fractional differential equations .pdf?sequence=1

by TT Hartley - 1996 - Cited by 165

http://gltrs.grc.nasa.gov/reports/1996/TP-3543.pdf

by NJ Ford - Cited by 5

http://www.evolutionedge.com/resources/chester/maths/pub/rep386.pdf

by R Garrappa - 2007 - Cited by 1

http://www.m-hikari.com/imf-password2007/13-16-2007/garrappaIMF13-16-2007.pdf

Numerical simulations confirm the ability of the controller to stabilize the fixed points in uncertain chaotic systems. ... recent years, the emergence of effective methods to ... 2 includes basic concepts in fractional calculus and fractional order systems. ..... Grigoriadis, K. Static output feedback: a survey. ...

http://pep.metapress.com/index/V2JN55451G481540.pdf

Methods and Special Functions, AUBG'99. Fractional Calculus & Applied Analysis 2, ...... Therefore, also an efficient numerical method to calculated vibrations of ... Based on a survey of fuel saving methods related to alternative ...

http://www.em.tue.nl/pdfs/Dissertations_2001.pdf

by A Bultheel - Cited by 14

https://lirias.kuleuven.be/bitstream/123456789/133551/1/frft2.pdf