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Fractional calculus: Resources


  1. I. Podlubny: Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications. Academic Press, San Diego-Boston-New York-London-Tokyo-Toronto, 1999, 368 pages, ISBN 0125588402.
  2. New: R. Caponetto, G. Dongola, L. Fortuna, I. Petras: Fractional Order Systems: Modeling and Control Applications. World Scientific, Singapore, 2010, 200 pages, ISBN-10: 9814304190, ISBN-13: 978-9814304191.
  3. I. Petras, I. Podlubny, P. O'Leary, L. Dorcak, B. Vinagre: Analogue Realization of Fractional Order Controllers. FBERG, Technical University of Kosice, Kosice, 2002, 84 pages, ISBN 8070996277.
  4. K.B. Oldham, J. Spanier: Fractional Calculus: Theory and Applications, Differentiation and Integration to Arbitrary Order. Academic Press, Inc., New York-London, 1974, 234 pages, ISBN 0125255500.
  5. K.S. Miller, B. Ross: An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley and Sons, Inc., 1993, 384 pages, ISBN 0471588849.
  6. B. Ross (Editor): Fractional Calculus and Its Applications: Proceedings of the International Conference, New Haven, June 1974. Springer-Verlag New York, Inc., New York, 1974, 380 pages, ISBN 038707161X.
  7. S.G. Samko, A.A. Kilbas, O.I. Marichev: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, 1993, 1006 pages, ISBN 2881248640.
  8. B. Bonilla, A. Kilbas, J. Trujillo: Calculo Fraccionario y Ecuaciones Diferenciales Fraccionarias. UNED Ediciones, Madrid, 2003, ISBN 8436248937 (in Spanish).
  9. New: F. Mainardi: Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. Imperial College Press, London, 2010, 368 pages, ISBN-10: 1848163290, ISBN-13: 978-1848163294.
  10. A. Carpinteri, F. Mainardi (Editors). Fractals and Fractional Calculus in Continuum Mechanics. CISM International Centre for Mechanical Sciences Series, vol. 378. Springer-Verlag New York, Inc., New York, 1997, 348pp, ISBN 321182913X.
    • Chapter on Fractional Calculus by R. Gorenflo and F. Mainardi [PDF]
    • Chapter on numerical methods of Fractional Calculus by R. Gorenflo [PDF]
    • Chapter by F. Mainardi on Fractional Calculus : Some Basic Problems in Continuum and Statistical Mechanics [Gzipped Postscript]
  11. R. Hilfer (Editor): Applications of Fractional Calculus in Physics. World Scientific Pub Co, Singapore, 2000, 463 pages, ISBN 9810234570.
  12. New: R. Magin: Fractional Calculus in Bioengineering. Begell House Inc., Redding, CT, 2006, 684 pages, ISBN-10: 1567002153, ISBN-13: 978-1567002157.
  13. R. Magin: Fractional Calculus in Bioengineering. Part 1-3. Critical Reviews in Bioengineering, vol. 32, 2004, ISSN 0278-940X, in total 380 pages in three journal issues.
  14. B. J. West, M. Bologna, P. Grigolini: Physics of Fractal Operators. Springer-Verlag, New York, 2003, 368 pages, ISBN 0387955542.
  15. S. Westerlund: Dead Matter has Memory! Causal Consulting, Kalmar, Sweden, 2002, x+220 pages, ISBN 9163123320.
  16. G. M. Zaslavsky: Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, 2005, 421 pages, ISBN 0198526040.
  17. G. M. Zaslavsky: Chaos, Fractional Kinetics, and Anomalous Transport, Physics Reports, vol. 371, 2002, pp. 461-580. — [PDF]
  18. V. Kiryakova: Generalized Fractional Calculus and Applications. Pitman Research Notes in Mathematics, vol. 301. Longman, Harlow, 360 pages, ISBN 0582219779.
  19. B. Rubin: Fractional Integrals and Potentials. Pitman Monographs and Surveys in Pure and Applied Mathematics, vol.82, Longman, Harlow, 1996, 424 pages, ISBN 0582253411.
  20. A.C. McBride: Fractional Calculus and Integral Transforms of Generalized Functions. Pitman Press, San Francisco, 1979, 179 pages, ISBN: 0273084151.
  21. H.M. Srivastava, S. Owa (Editors): Univalent Functions, Fractional Calculus and Their Applications. Prentice Hall, 1989, 404 pages, ISBN 0470216301.
  22. K. Nishimoto: Fractional Calculus: Integrations and Differentiations of Arbitrary Order. University of New Haven Press, New Haven, 1989, ISBN 9990036381.
  23. H.M. Srivastava and R.G. Buschman: Theory and Applications of Convolution Integral Equations, Kluwer Series on Mathematics and Its Applications, vol. 79, Kluwer Academic Publishers, Dordrecht, Boston, and London, 1992, ISBN 0792318919.
  24. A. Oustaloup: La Derivation Non Entiere: Theorie, Synthese et Applications, Hermes, Paris, 1995, ISBN 2866014561.
  25. A. Oustaloup, B. Mathieu: La Commande CRONE, Hermes, Paris, 1991.
  26. A. Oustaloup: Systèmes asservis linéaires d'ordre fractionnaire: théorie et pratique. Masson, Paris, 1983.
  27. M.W. Michalski: Derivatives of noninteger order and their applications. Dissertationes Mathematicae, CCCXXVIII, Inst. Math., Polish Acad. Sci., Warsaw, 1993.
  28. M.M. Dzhrbashyan: Integral Transforms and Representations of Functions in the Complex Domain, Nauka, Moscow, 1966 (in Russian).
  29. M. Caputo: Elasticita e Dissipazione, Zanichelli, Bologna, 1969.
  30. M. Caputo: Lectures on Seismology and Rheological Tectonics. Univ. degli studi di Roma “La Sapienza”, 1992–1993. — [PDF]
  31. Yu.I. Babenko: Heat and Mass Transfer. Khimiya, Leningrad, 1986 (in Russian).

Chapters in books

  1. A. I. Tseytlin: Applied Methods of Solution of Boundary Value Problems in Civil Engineering, Stroyizdat, Moscow,1984 (in Russian).
  2. Yu. N. Rabotnov: Elements of Hereditary Solids Mechanics, Mir Publishers, Moscow, 1980,  387 pages. [Rev. from the 1977 Russian ed.]
  3. Yu. N. Rabotnov: Creep of Structural Elements, Nauka, Moscow, 1966 (in Russian).
  4. C. M. Case: Physical Principles of Flow in Unsaturated Porous Media, Clarendon Press, Oxford, 1994. (see Section 5.3).  xiv+372 pages, ISBN 0195046226. 
  5. A. I. Saichev, W. A. Woyczynski: Distributions in the Physical and Engineering Sciences, vol. 1,  Birkhauser, Boston, 1997,  x+336 pages, ISBN 0817639241. (see Chapter 6).
  6. Xue Ding Yu, YangQuan Chen: Solution of Advanced Problems of Applied Mathematics with MATLAB. Qinghua, 2004, 420 pages, ISBN 7302093113. (in Chinese). -- see Chapter 10.
  7. V. Blondel, A. Megretski (Eds.): Unsolved Problems in Mathematical Systems and Control Theory. Prinston University Press, 2004, 360 pp., ISBN 0691117489 (Available on-line)

Special journal issues on fractional calculus and its applications

  1. Fractional Differential Systems: Models, Methods and Applications. ESAIM Proceedings, Vol. 5, 1998, 1-204.
  2. Special Issue of Fractional Order Calculus and Its Applications. Nonlinear Dynamics, July–September 2002, Volume 29, Issue 1-4.
  3. Special Issue on Strange Kinetics. Chemical Physics, Volume 284, Issues 1-2, Pages 1-541 (1 November 2002).
  4. Special Issue on Fractional Signal Processing and Applications. Signal Processing, Volume 83, Issue 11, Pages 2285-2480 (November 2003).
  5. Special Issue of Fractional Order Derivatives and their Applications. Nonlinear Dynamics, December 2004, Volume 38, Issue 1-2.
  6. Special Issue on Fractional Calculus Applications in Signals and Systems Signal Processing, Volume 86, Issue 10, Pages 2503-3094 (October 2006)

Specialized journals

  1. Fractional Calculus & Applied Analysis
  2. Fractals
  3. Chaos, Solitons, and Fractals
  4. Journal of Mathematical Analysis and Applications