Recent history of fractional calculus

By K. B. Oldham, J. Spanier, Alain Oustaloup. 2011

1,118 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c29dfec3f2beeb9bb085863963b7d22964358822

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Citations in the corpus

Review of Some Promising Fractional Physical Models (2013, background): “It has a long history [1, 2, 3] from 30 September 1695, when the derivatives of order α = 1/2 has been described by Leibniz in a letter to L’Hospital.”
The Chronicles of Fractional Calculus (2017, background): “, have been provided in our previous survey of 2011, [105].”
Science metrics on fractional calculus development since 1966 (2013, background): “Fractional Calculus (FC) started in 1695 based on Gottfried Leibniz ideas and, since then, many relevant scientists supported its continuous progress, see for example the surveys [18, 49].”
Elasticity for economic processes with memory: Fractional differential calculus approach (2016, background): “Introduction Theory of derivatives and integrals of non-integer (fractional) orders [1, 2, 3, 4] has a long history [5, 6].”
On chain rule for fractional derivatives (2016, background): “Derivatives and integrals of non-integer orders [1–3] have a long history [1,4–8].”
An efficient collocation method for a Caputo two-point boundary value problem (2015, background): “The mathematical analysis of problems involving these derivatives has also attracted much attention—a survey of recent activity is given in [8].”
Fractional Calculus: Quo Vadimus? (Where are we Going?) (2015, result): “We have taken the present occasion, as a compliment to our previous survey [107], to cite books published during the years 2011 [92, 80, 44, 26, 65, 47, 5, 106, 117], 2012 [7, 3, 77, 1, 51, 38, 102, 56, 122, 15, 112, 110, 118], 2013 [14, 18, 89, 29, 36], and 2014 [57, 4, 121, 39, 105, 40, 66, 86, 2,”
Fractional differential equations: a novel study of local and global solutions in Banach spaces (2013, background): “With this answer, formally the fractional calculus was born [42, 47].”
Certain Fractional Integral Operators and the Generalized Incomplete Hypergeometric Functions (2013, background): “…were studied by Saigo and Maeda (Saigo and Maeda, 1998) (see also some recent investigations on the subject of fractional calculus in (Agarwal, 2012a; Agarwal, 2012b; Agarwal and Jain, 2011; J. A. T. Machado and Mainardi, 2010; J. A. T. Machado and Mainardi, 2011; S. D. Purohit and Kalla, 2011)).”
Non-instantaneous impulses in Caputo fractional differential equations (2017, background): “For more details on geometric and physical interpretations of fractional derivatives and for a general historical perspective, we refer the reader to the monographs [18, 31, 33], to the survey papers [37, 38], and the cited references therein.”
Extended Riemann-Liouville fractional derivative operator and its applications (2015, background): “The review-cum-survey paper [13] is gladly recommended for the readers who would like to know some of the major documents and events in the area of fractional calculus that took place since 1974 up to 2010.”
Spline collocation methods for seismic analysis of multiple degree of freedom systems with visco-elastic dampers using fractional models (2020, positive): “It generalizes the notions of integer-order differentiation and n-fold integration (Atangana and Baleanu, 2016; Baleanu et al., 2011, 2012; Diethelm, 2010; Edwards et al., 2002; Gemant, 1936; Gorenflo and Mainardi, 1997; Kilbas et al., 2006; Magin, 2006; Podlubny, 1999; Sabatier et al., 2007; Tenrei”
Some pioneers of the applications of fractional calculus (2013, background): “We can list (in alphabetical order) some important researchers since 1695 (see details at [1, 2, 3], and posters at http://www.”