članak: 1 od 1  
Publikacija Elektrotehničkog fakulteta - serija: matematika
2002, br. 13, str. 77-84
jezik rada: engleski
neklasifikovan
doi:10.2298/PETF0213077T
On some fractional derivatives of functions of exponential type
(naslov ne postoji na srpskom)
Trenčevski Kostadin, Tomovski Živorad
Institute of Mathematics, St. Cyril and Methodius University, Skopje, Macedonia

e-adresa: kostatre@iunona.pmf.ukim.edu.mk

Sažetak

(ne postoji na srpskom)
In this paper a new proof of the well known fact that the derivative of e " of order α ∈ R is equal to λαeλx is given. It enables to conclude that sin(α)(x) = sin(x + απ/2) and cos(α)(x) = cos (x + απ/2) which is initial assumption (axiom) for the classical theory of fractional derivatives. Namely we use a new method for calculation of fractional derivatives of functions of exponential type.

Ključne reči

fractional derivatives; exponential function

Reference

Mitrinović, D.S., Kečkić, J.D. (1990) Metodi izračunavanja konačnih zbirova. Beograd

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Samko, S.G., Kilbas, A.A., Marichev, O.I. (1987) Integrals and fractional derivatives and some of their applications. Minsk, in Russian

Spiegel, M.R. (1988) Theory and problems of complex variables. Singapore

MathSciNetKoBSON

Tomovski, Ž., Trenčevski, K. (2002) A solution of one problem of complex integration. Tamkang J. Math, 33, 2, 103-107

Trenčevski, K., Tomovski, Ž. (2002) A solution of one old problem. Matematika Makedonika, (to appear)