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Fractional calculus: Resources

Books

  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. 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.
  3. 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.
  4. 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.
  5. 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.
  6. S.G. Samko, A.A. Kilbas, O.I. Marichev: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, 1993, 1006 pages, ISBN 2881248640.
  7. New: B. Bonilla, A. Kilbas, J. Trujillo: Calculo Fraccionario y Ecuaciones Diferenciales Fraccionarias. UNED Ediciones, Madrid, 2003, ISBN 8436248937 (in Spanish).
  8. 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.
    • New: Chapter on Fractional Calculus by R. Gorenflo and F. Mainardi [PDF]
    • New: Chapter on numerical methods of Fractional Calculus by R. Gorenflo [PDF]
    • New: Chapter by F. Mainardi on Fractional Calculus : Some Basic Problems in Continuum and Statistical Mechanics [Gzipped Postscript]
  9. R. Hilfer (Editor): Applications of Fractional Calculus in Physics. World Scientific Pub Co, Singapore, 2000, 463 pages, ISBN 9810234570.
  10. New: 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.
  11. B. J. West, M. Bologna, P. Grigolini: Physics of Fractal Operators. Springer-Verlag, New York, 2003, 368 pages, ISBN 0387955542.
  12. S. Westerlund: Dead Matter has Memory! Causal Consulting, Kalmar, Sweden, 2002, x+220 pages, ISBN 9163123320.
  13. New: G. M. Zaslavsky: Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, 2005, 421 pages, ISBN 0198526040.
  14. G. M. Zaslavsky: Chaos, Fractional Kinetics, and Anomalous Transport, Physics Reports, vol. 371, 2002, pp. 461-580. — [PDF]
  15. V. Kiryakova: Generalized Fractional Calculus and Applications. Pitman Research Notes in Mathematics, vol. 301. Longman, Harlow, 360 pages, ISBN 0582219779.
  16. B. Rubin: Fractional Integrals and Potentials. Pitman Monographs and Surveys in Pure and Applied Mathematics, vol.82, Longman, Harlow, 1996, 424 pages, ISBN 0582253411.
  17. A.C. McBride: Fractional Calculus and Integral Transforms of Generalized Functions. Pitman Press, San Francisco, 1979, 179 pages, ISBN: 0273084151.
  18. H.M. Srivastava, S. Owa (Editors): Univalent Functions, Fractional Calculus and Their Applications. Prentice Hall, 1989, 404 pages, ISBN 0470216301.
  19. K. Nishimoto: Fractional Calculus: Integrations and Differentiations of Arbitrary Order. University of New Haven Press, New Haven, 1989, ISBN 9990036381.
  20. 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.
  21. A. Oustaloup: La Derivation Non Entiere: Theorie, Synthese et Applications, Hermes, Paris, 1995, ISBN 2866014561.
  22. A. Oustaloup, B. Mathieu: La Commande CRONE, Hermes, Paris, 1991.
  23. A. Oustaloup: Systèmes asservis linéaires d'ordre fractionnaire: théorie et pratique. Masson, Paris, 1983.
  24. M.W. Michalski: Derivatives of noninteger order and their applications. Dissertationes Mathematicae, CCCXXVIII, Inst. Math., Polish Acad. Sci., Warsaw, 1993.
  25. M.M. Dzhrbashyan: Integral Transforms and Representations of Functions in the Complex Domain, Nauka, Moscow, 1966 (in Russian).
  26. M. Caputo: Elasticita e Dissipazione, Zanichelli, Bologna, 1969.
  27. M. Caputo: Lectures on Seismology and Rheological Tectonics. Univ. degli studi di Roma “La Sapienza”, 1992–1993. — [PDF]
  28. Yu.I. Babenko: Heat and Mass Transfer. Khimiya, Leningrad, 1986 (in Russian).

New: 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. New: 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. New: V. Blondel, A. Megretski (Eds.): Unsolved Problems in Mathematical Systems and Control Theory. Prinston University Press, 2004, 360 pp., ISBN 0691117489 (Available on-line)

New: 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. New: 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