Science metrics on fractional calculus development since 1966

During the last fifty years the area of Fractional Calculus verified a considerable progress. This paper analyzes and measures the evolution that occurred since 1966.

[1]  J. Huisman The Netherlands , 1996, The Lancet.

[2]  J. A. Tenreiro Machado,et al.  Nonlinear Science and Complexity , 2011 .

[3]  Y. Xiaojun,et al.  Advanced Local Fractional Calculus and Its Applications , 2012 .

[4]  Anatoly A. Kilbas,et al.  Analytic methods of analysis and differential equations : AMADE 2006 , 2006 .

[5]  José António Tenreiro Machado,et al.  Fractional calculus applications in signals and systems , 2006, Signal Processing.

[6]  A. M. Mathai,et al.  Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences , 1973 .

[7]  D. Valério,et al.  An Introduction to Fractional Control , 2012 .

[8]  Jürgen Kurths,et al.  Fractional calculus and its applications , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[9]  Mahmoud H. Annaby,et al.  q-Fractional Calculus and Equations , 2012 .

[10]  V. Kiryakova Generalized Fractional Calculus and Applications , 1993 .

[11]  A. Kilbas H-Transforms: Theory and Applications , 2004 .

[12]  J. A. Tenreiro Machado,et al.  A Poster about the Old History of Fractional Calculus , 2010 .

[13]  Jean-Paul Chilès,et al.  Wiley Series in Probability and Statistics , 2012 .

[14]  B. West Fractional Calculus in Bioengineering , 2007 .

[15]  A. Mcbride,et al.  Fractional calculus and integral transforms of generalized functions , 1979 .

[16]  Arak M. Mathai,et al.  Special Functions for Applied Scientists , 2008 .

[17]  Prakasa Rao,et al.  Statistical Inference for Fractional Diffusion Processes: Rao/Statistical Inference for Fractional Diffusion Processes , 2010 .

[18]  R. Hilfer Applications Of Fractional Calculus In Physics , 2000 .

[19]  Ralf Metzler,et al.  Fractional Calculus: An Introduction for Physicists , 2012 .

[20]  Niels Jacob,et al.  Pseudo-Differential Operators and Markov Processes , 1996 .

[21]  Blanca Nieves Bonilla de Paz,et al.  Cálculo fraccionario y ecuaciones diferenciales fraccionarias , 2003 .

[22]  Y. Chen,et al.  Fractional Order Motion Controls , 2012 .

[23]  Mouffak Benchohra,et al.  Topics in Fractional Differential Equations , 2012 .

[24]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .

[25]  B. Ross,et al.  Fractional Calculus and Its Applications , 1975 .

[26]  Igor M. Sokolov,et al.  Physics of Fractal Operators , 2003 .

[27]  R. Gorenflo,et al.  Abel Integral Equations: Analysis and Applications , 1991 .

[28]  J. A. Tenreiro Machado,et al.  Intelligent Engineering Systems and Computational Cybernetics , 2010 .

[29]  St'ephane Dugowson,et al.  Les différentielles métaphysiques : histoire et philosophie de la généralisation de l'ordre de la dérivation , 1994 .

[30]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[31]  J. A. Tenreiro Machado,et al.  New Trends in Nanotechnology and Fractional Calculus Applications , 2010 .

[32]  R. Sibatov,et al.  Fractional Kinetics in Solids: Anomalous Charge Transport in Semiconductors, Dielectrics and Nanosystems , 2012 .

[33]  Saptarshi Das,et al.  Fractional Order Signal Processing: Introductory Concepts and Applications , 2011 .

[34]  I. Podlubny,et al.  Analogue Realizations of Fractional-Order Controllers , 2002 .

[35]  Ivan Nourdin,et al.  Selected Aspects of Fractional Brownian Motion , 2013 .

[36]  George B. Arfken,et al.  More Special Functions , 2012 .

[37]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[38]  A. Oustaloup La dérivation non entière , 1995 .

[39]  Ivo Petras,et al.  Fractional-Order Nonlinear Systems , 2011 .

[40]  S. Yau Mathematics and its applications , 2002 .

[41]  V. Zolotarev,et al.  Chance and Stability, Stable Distributions and Their Applications , 1999 .

[42]  Y. Chen,et al.  Fractional Processes and Fractional-Order Signal Processing , 2012 .

[43]  Mathematical Methods in Engineering , 2007 .

[44]  I. Petráš Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation , 2011 .

[45]  Yangquan Chen,et al.  Distributed-Order Dynamic Systems - Stability, Simulation, Applications and Perspectives , 2012, Springer Briefs in Electrical and Computer Engineering.

[46]  I. Podlubny Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[47]  A. Luo,et al.  Fractional Dynamics and Control , 2011 .

[48]  G.E. Moore,et al.  Cramming More Components Onto Integrated Circuits , 1998, Proceedings of the IEEE.

[49]  Arak M. Mathai,et al.  The H-function with applications in statistics and other disciplines , 1978 .

[50]  Agnieszka B. Malinowska,et al.  Introduction to the Fractional Calculus of Variations , 2012 .

[51]  Manuel Duarte Ortigueira,et al.  Fractional Calculus for Scientists and Engineers , 2011, Lecture Notes in Electrical Engineering.

[52]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[53]  S. Westerlund Dead matter has memory , 1991 .

[54]  Ralf Metzler,et al.  Fractional dynamics : recent advances , 2011 .

[55]  K. Diethelm,et al.  Fractional Calculus: Models and Numerical Methods , 2012 .

[56]  F. Mainardi Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models , 2010 .

[57]  Hossein Jafari,et al.  Fractional calculus: theory and numerical methods , 2013 .

[58]  Z. K. Silagadze,et al.  Citations and the Zipf-Mandelbrot Law , 1999, Complex Syst..

[59]  Boris Rubin,et al.  Fractional Integrals and Potentials , 1996 .

[60]  YangQuan Chen,et al.  Linear Feedback Control: Analysis and Design with MATLAB , 2008 .

[61]  F. Mainardi,et al.  Fractals and fractional calculus in continuum mechanics , 1997 .

[62]  B. P. Rao Statistical Inference for Fractional Diffusion Processes: Rao/Statistical Inference for Fractional Diffusion Processes , 2010 .

[63]  A. M. Mathai,et al.  The H-Function: Theory and Applications , 2009 .

[64]  I. Sokolov,et al.  Anomalous transport : foundations and applications , 2008 .

[65]  西本 勝之 Nishimoto's fractional calculus : calculus in the 21st century : integrations and differentiations of arbitrary order , 1991 .

[66]  V. E. Tarasov Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media , 2011 .

[67]  Jozsef K. Tar,et al.  New Challenges in Fractional Systems , 2013 .

[68]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[69]  Timothy Margulies Mathematics & science applications & frontiers : with fractional calculus , 2008 .

[70]  V. Lakshmikantham,et al.  Theory of Fractional Dynamic Systems , 2009 .

[71]  Y. Chen,et al.  Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications , 2011 .

[72]  M. Meerschaert,et al.  Stochastic Models for Fractional Calculus , 2011 .

[73]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[74]  José António Tenreiro Machado,et al.  Fractional differentiation and its applications I , 2013, Comput. Math. Appl..

[75]  Saptarshi Das,et al.  Intelligent Fractional Order Systems and Control - An Introduction , 2012, Studies in Computational Intelligence.

[76]  William R. Young,et al.  Strongly and weakly self-similar diffusion , 2001 .

[77]  Francesco Mainardi,et al.  A Poster about the Recent History of Fractional Calculus , 2010 .

[78]  YangQuan Chen,et al.  Solving Applied Mathematical Problems with MATLAB , 2008 .

[79]  Alan D. Freed,et al.  Fractional-order Viscoelasticity (FOV): Constitutive Development Using the Fractional Calculus: First Annual Report , 2002 .

[80]  Arak M. Mathai,et al.  Proceedings of the third UN/ESA/NASA Workshop on the International Heliophysical Year 2007 and basic space science : National Astronomical Observatory of Japan , 2010 .

[81]  A. Oustaloup,et al.  La commande crone : du scalaire au multivariable , 1999 .

[82]  Hari M. Srivastava,et al.  The H-functions of one and two variables, with applications , 1982 .

[83]  Hari M. Srivastava,et al.  Theory and Applications of Convolution Integral Equations , 1992 .

[84]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[85]  J. Klafter,et al.  First Steps in Random Walks: From Tools to Applications , 2011 .

[86]  George M. Zaslavsky Hamiltonian Chaos and Fractional Dynamics , 2005 .

[87]  W. Snodgrass Physiology , 1897, Nature.

[88]  Oleg G. Bakunin,et al.  Turbulence and Diffusion: Scaling Versus Equations , 2008 .

[89]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[90]  K. Diethelm The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .

[91]  Yuri Luchko,et al.  The Hypergeometric Approach to Integral Transforms and Convolutions , 1994 .

[92]  I︠u︡. A Brychkov Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas , 2008 .

[93]  A. Oustaloup Systèmes asservis linéaires d'ordre fractionnaire : théorie et pratique , 1983 .

[94]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[95]  Hari M. Srivastava,et al.  Univalent Functions, Fractional Calculus, and Their Applications , 1990, The Mathematical Gazette.

[96]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[97]  Yang Xiao-Jun Local Fractional Functional Analysis and Its Applications , 2011 .

[98]  Alfred J. Lotka,et al.  The frequency distribution of scientific productivity , 1926 .

[99]  José António Tenreiro Machado,et al.  New trends in fractional dynamics , 2014 .

[100]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[101]  Q. Naqvi,et al.  Electromagnetic Fields and Waves in Fractional Dimensional Space , 2012 .

[102]  P. Lorrain,et al.  Electromagnetic fields and waves , 1970 .

[103]  Alessandro Pisano,et al.  Special Issue on “Advances in Fractional Order Control and Estimation” , 2013 .