Remarks on the Caputo fractional derivative

• Autorzy: Sikora Beata
• Języki publikacji: EN

Abstrakty

EN

The purpose of the paper is to familiarise the reader with the concept of the Caputo fractional derivative. The definition and basic properties of the Caputo derivative are given. Formulas for the derivatives of selected functions are derived. Examples of calculating the derivatives of basic functions are presented. The paper also contains a number of self-solving exercises, with answers.

Słowa kluczowe

EN

fractional derivative; Caputo derivative; fractional calculus

PL

pochodna ułamkowa; pochodna Caputo; rachunek ułamkowy

• Wydawca: Politechnika Śląska, Wydział Matematyki Stosowanej, Katedra Matematyki
• Czasopismo: MINUT Matematyka i Informatyka na Uczelniach Technicznych
• Rocznik: 2023
• Tom: Nr 5
• Strony: 76--84
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Sikora Beata

• Faculty of Applied Mathematics, Silesian University of Technology

Bibliografia

• 1. R. Almeida, N.R.O. Bastos, M.T.T. Monteiro, Modeling some real phenomena by fractional differential equations (Special Issue Paper), Mathematical Methods in the Applied Sciences 39 (16), 2015.
• 2. M. Caputo, Linear Models of Dissipation whose Q is almost Frequency Independent-II, Geophys. J. R. Astr. Soc. 13 (1967), pp. 529-539.
• 3. K. Diethelm, N.J. Ford, A.D. Freed, Y. Luchko, Algorithms for the fractional calculus: A selection of numerical methods, Computer methods in applied mechanics and engineering 194 (2005), pp. 743-773.
• 4. K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Series on Complexity, Nonlinearity and Chaos, Springer, Heidelberg, 2010.
• 5. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
• 6. M.K. Ishteva, Properties and Applications of the Caputo Fractional Operator (Master Thesis), Department of Mathematics, Karlsruhe Institute of Technology, 2005.
• 7. A. A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, 2006.
• 8. K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential calculus, Villey, 1993.
• 9. G. W. Leibnitz, Leibnitzen's Mathematische Schriften, Hildesheim, Germany: Georg Olm 2 (1962), pp. 301-302.
• 10. J. Liouville, Mémoire sur quelques Quéstions de Géometrie et de Mécanique, et sur un nouveau genre de Calcul pour résoudre ces Quéstions, Journal de l'École Polytechnique 13 (1832), pp. 1-69.
• 11. K.B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York 1974.
• 12. M.D. Ortigueira, J.A. Tenreiro Machado, What is a fractional derivative?, Journal of Computational Physics 293 (2015), pp. 4-13.
• 13. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Mathematics in Science and Engineering, Academic Press, 1999.
• 14. B. Ross, Fractional Calculus and its Applications, Springer Lecture Notes in Mathematics 57 (1975), pp. 1-36.
• 15. B. Ross, The Development of the Gamma Function and A Profile of Fractional Calculus, New York University dissertation, New York 1974.
• 16. S. G. Samko, A.A. Kilbas, O.I. Marichev, Fractional integrals and derivatives: theory and applications, Gordan and Breach Science Publishers, 1993.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).