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The Fractional Calculus of Sets (FCS), first introduced in the article titled "Sets of Fractional Operators and Numerical Estimation of the Order of Convergence of a Family of Fractional Fixed-Point Methods"[1], is a methodology derived from fractional calculus[2]. The primary concept behind FCS is the characterization of fractional calculus elements using sets due to the plethora of fractional operators available.[3][4][5]. This methodology originated from the development of the Fractional Newton-Raphson method[6] and subsequent related works.[7][8][9][10].
- ^ Torres-Hernandez, A.; Brambila-Paz, F. (December 29, 2021). "Sets of Fractional Operators and Numerical Estimation of the Order of Convergence of a Family of Fractional Fixed-Point Methods". Fractal and Fractional. 5 (4): 240. doi:10.3390/fractalfract5040240.
- ^ Hilfer, Rudolf (2 March 2000). Applications of fractional calculus in physics. World Scientific. ISBN 978-981-4496-20-9.
- ^ de Oliveira, Edmundo Capelas; Tenreiro Machado, José António (June 10, 2014). "A Review of Definitions for Fractional Derivatives and Integral". Mathematical Problems in Engineering. 2014: e238459. doi:10.1155/2014/238459.
- ^ Sales Teodoro, G.; Tenreiro Machado, J.A.; Capelas de Oliveira, E. (July 29, 2019). "A review of definitions of fractional derivatives and other operators". Journal of Computational Physics. 388: 195–208. Bibcode:2019JCoPh.388..195S. doi:10.1016/j.jcp.2019.03.008.
- ^ Valério, Duarte; Ortigueira, Manuel D.; Lopes, António M. (January 29, 2022). "How Many Fractional Derivatives Are There?". Mathematics. 10 (5): 737. doi:10.3390/math10050737.
- ^ Torres-Hernandez, A.; Brambila-Paz, F. (2021). "Fractional Newton-Raphson Method". Applied Mathematics and Sciences an International Journal (Mathsj). 8: 1–13. doi:10.5121/mathsj.2021.8101.
- ^ Torres-Hernandez, A.; Brambila-Paz, F.; Montufar-Chaveznava, R. (September 29, 2022). "Acceleration of the order of convergence of a family of fractional fixed-point methods and its implementation in the solution of a nonlinear algebraic system related to hybrid solar receivers". Applied Mathematics and Computation. 429: 127231. arXiv:2109.03152. doi:10.1016/j.amc.2022.127231. hdl:10230/60337.
- ^ Torres-Hernandez, A. (2022). "Code of a multidimensional fractional quasi-Newton method with an order of convergence at least quadratic using recursive programming". Applied Mathematics and Sciences an International Journal (MathSJ). 9: 17–24. doi:10.5121/mathsj.2022.9103.
- ^ Torres-Hernandez, A.; Brambila-Paz, F.; Ramirez-Melendez, R. (2022). "Sets of Fractional Operators and Some of Their Applications". Operator Theory - Recent Advances, New Perspectives and Applications.
- ^ Torres-Hernandez, Anthony; Brambila-Paz, Fernando; Ramirez-Melendez, Rafael (January 2024). "Proposal for Use of the Fractional Derivative of Radial Functions in Interpolation Problems". Fractal and Fractional. 8 (1): 16. doi:10.3390/fractalfract8010016. ISSN 2504-3110.