分数階微積分学
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分数階偏微分
脚注
参考文献
- Fractional Integrals and Derivatives: Theory and Applications, by Samko, S.; Kilbas, A.A.; and Marichev, O. Hardcover: 1006 pages. Publisher: Taylor & Francis Books. ISBN 2-88124-864-0
- Theory and Applications of Fractional Differential Equations, by Kilbas, A. A.; Srivastava, H. M.; and Trujillo, J. J. Amsterdam, Netherlands, Elsevier, February 2006. ISBN 0-444-51832-0 (http://www.elsevier.com/wps/find/bookdescription.cws_home/707212/description#description)
- An Introduction to the Fractional Calculus and Fractional Differential Equations, by Kenneth S. Miller, Bertram Ross (Editor). Hardcover: 384 pages. Publisher: John Wiley & Sons; 1 edition (May 19, 1993). ISBN 0-471-58884-9
- The Fractional Calculus; Theory and Applications of Differentiation and Integration to Arbitrary Order (Mathematics in Science and Engineering, V), by Keith B. Oldham, Jerome Spanier. Hardcover. Publisher: Academic Press; (November 1974). ISBN 0-12-525550-0
- Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications., (Mathematics in Science and Engineering, vol. 198), by Igor Podlubny. Hardcover. Publisher: Academic Press; (October 1998) ISBN 0-12-558840-2
- Fractional Calculus - An Introduction for Physicists by R. Herrmann, World Scientific, Singapore 2014. 500 pages.
- Fractals and quantum mechanics, by N. Laskin. Chaos Vol.10, pp.780-790 (2000). (http://link.aip.org/link/?CHAOEH/10/780/1)
- Fractals and Fractional Calculus in Continuum Mechanics, by A. Carpinteri (Editor), F. Mainardi (Editor). Paperback: 348 pages. Publisher: Springer-Verlag Telos; (January 1998). ISBN 3-211-82913-X
- Physics of Fractal Operators, by Bruce J. West, Mauro Bologna, Paolo Grigolini. Hardcover: 368 pages. Publisher: Springer Verlag; (January 14, 2003). ISBN 0-387-95554-2
- Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. by F. Mainardi, Imperial College Press, 2010. 368 pages.
- Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. by V.E. Tarasov, Springer, 2010. 450 pages.
- Fractional Derivatives for Physicists and Engineers by V.V. Uchaikin, Springer, Higher Education Press, 2012, 385 pages.
- Fractional Calculus and the Taylor-Riemann Series, Rose-Hulman Undergrad. J. Math. Vol.6(1) (2005).
- Operator of fractional derivative in the complex plane, by Petr Zavada, Commun.Math.Phys.192, pp. 261-285,1998. doi:10.1007/s002200050299 (available online or as the arXiv preprint)
- Relativistic wave equations with fractional derivatives and pseudodifferential operators, by Petr Zavada, Journal of Applied Mathematics, vol. 2, no. 4, pp. 163-197, 2002. doi:10.1155/S1110757X02110102 (available online or as the arXiv preprint)
- Fractional differentiation by neocortical pyramidal neurons, by Brian N Lundstrom, Matthew H Higgs, William J Spain & Adrienne L Fairhall, Nature Neuroscience, vol. 11 (11), pp. 1335 - 1342, 2008. doi:10.1038/nn.2212 (abstract)
- Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models, by Ahmed E., A.M.A. El-Sayed, H.A.A. El-Saka. 2007. Jour. Math. Anal. Appl. 325,452.
関連項目
- ^ ここで積分作用素の J は integration の頭文字 I を用いるところ、I は恒等写像など他の意味に使われたり、I に似た字形の記号・文字がいろいろと使われたりすることによる混同を避けるためにしばしば使われる。
- ^ Liouville, Joseph (1832), “Mémoire sur quelques questions de géométrie et de mécanique, et sur un nouveau genre de calcul pour résoudre ces questions”, Journal de l'École Polytechnique (Paris) 13: 1-69.
- ^ Liouville, Joseph (1832), “Mémoire sur le calcul des différentielles à indices quelconques”, Journal de l'École Polytechnique (Paris) 13: 71-162.
- ^ この主題の歴史については、以下の修士論文(フランス語)Stéphane Dugowson, Les différentielles métaphysiques (histoire et philosophie de la généralisation de l'ordre de dérivation), Thèse, Université Paris Nord (1994) を参照。
- ^ Hadamard, J. (1892), “Essai sur l'étude des fonctions données par leur développement de Taylor”, Journal of pure and applied mathematics 4 (8): 101–186
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