Niejednoznaczność zapisu dodatniej pochodno-całki Grünwalda-Letnikova
Ambiguous notation of Grünwald-Letnikov differintegral
Keywords:
differintegrals, Grünwald-Letnikov
Abstract
The paper discussed the problem of Grünwald-Letnikov differintegral notation in which non-integer order can be incorrectly interpreted as a higher or lower order derivative. Taking the problem into consideration the author’s proposal is new notation of differintegrals.
References
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2. Cioć R.: Grünwald-Letnikov derivative – analyse in space of first order derivative. Frontiers in Fractional Calculus, Book Series: Current Developments in Mathematical Sciences Vol. 1, eISBN: 978-1-68108-599-9, ISBN: 978-1-68108-600-2, ISSN: 2589-2711 (Print), ISSN: 2589-272X (Online), Bentham Science Publishers Ltd 2018.
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4. Das S.: Functional Fractional Calculus for System Identification and Controls. Springer-Verlag Berlin Heidelberg 2008.
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2. Cioć R.: Grünwald-Letnikov derivative – analyse in space of first order derivative. Frontiers in Fractional Calculus, Book Series: Current Developments in Mathematical Sciences Vol. 1, eISBN: 978-1-68108-599-9, ISBN: 978-1-68108-600-2, ISSN: 2589-2711 (Print), ISSN: 2589-272X (Online), Bentham Science Publishers Ltd 2018.
3. Cioć R.: Dodatnia pochodna Grünwalda-Letnikova jako pochodna funkcji drogi. Autobusy. Technika, Eksploatacja, Systemy Trans-portowe, 12/2017.
4. Das S.: Functional Fractional Calculus for System Identification and Controls. Springer-Verlag Berlin Heidelberg 2008.
5. Gómez-Aguilar J.F. et al.: A Physical Interpretation of Fractional Calculus in Observables Terms: Analysis of the Fractional Time Constant and the Transitory Response. Revista Mexicana de Física 60, 32-38, 2014.
6. Miller K., Bertram R.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley & Sons 1993.
7. Ostalczyk P.: Zarys rachunku różniczkowo-całkowego ułamkowych rzędów. Teoria i zastosowanie w praktyce. Wydawnictwo Politechniki Łódzkiej, Łódź 2008.
8. Podlubny I.: Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications. Academic Press, San Diego 1999.
9. Rutman R.S.: On Physical Interpretation of Fractional Integration and Differentiation. Theoretical and Mathematical Physics, Vol. 105, No. 3, 1995.
Published
2019-02-25
Issue
Section
Eksploatacja i Testy/Exploitation and Tests
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