Geometry of hypersurfaces in Euclidean 4-space with Caputo fractional derivatives
*Oumar DiopCorresponding authoroumardiop306@gmail.comDépartement de Mathématiques et InformatiqueFaculté des Sciences et TechniquesUniversite Cheikh Anta DiopDakar, SenegalView full profile → , Ameth Ndiayeameth1.ndiaye@ucad.edu.snDépartement de MathématiquesFaculté des Sciences et Technologies de l’Education et de la FormationUniversite Cheikh Anta DiopDakar, SenegalView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 04 Jul 2023
- Published Online:
- 05 May 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1794
- Pages:
- 1367–1384
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References
[1] M. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall (1976).
[2] F. Mainardi, “Fractional calculus: Some basic problems in continuum and statistical mechanics,” in CISM Courses and Lectures, vol. 378, Springer-Verlag, Berlin, pp. 291-348 (1997).
[3] M. E. Aydın, M. Bektaş, O. Öğrenmiş, O. Alper, and A. Yokus, “Differential geometry of curves in Euclidean 3-space with fractional order,” Int. J. Maps Math., vol. 4, no. 1, pp. 40-52 (2021).
[4] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999).
[5] Z. Baitiche and C. Derbazi, “Implicit fractional differential equations with ϕ-Caputo fractional derivative in Banach spaces,” J. Interdiscip. Math., vol. 25, no. 5, pp. 1237-1252 (2022), doi: 10.1080/09720502.2021.1961979.
[6] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier B.V., Amsterdam, The Netherlands (2006).
[7] T. Yajima, S. Oiwa, and K. Yamasaki, “Geometry of curves with fractional-order tangent vector and Frenet-Serret formulas,” Fract. Calc. Appl. Anal., vol. 21, no. 6, pp. 1493-1505 (2018).
[8] T. Yajima and K. Yamasaki, “Geometry of surfaces with Caputo fractional derivatives and applications to incompressible two-dimensional flows,” J. Phys. A: Math. Theor., vol. 45, no. 6, p. 065201, 15 pp. (2012).




