A study on nabla discrete fractional operator in mass - spring - damper system
Öz
The fractional
calculus that is one of the new trends in science and engineering is concept of
derivative and integral with arbitrary order. And, discrete fractional calculus
(DFC) has an important place in fractional calculus which studied for the last
300 years. In present paper, we solved the equations of motion in
mass-spring-damper system by using nabla (
) discrete fractional operator. And, we also introduced some instructive
examples.
Anahtar Kelimeler
Kaynakça
- K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press Cambridge, MA, USA (1974).
- J.B. Diaz and T.J. Osler, Differences of fractional order, American Mathematical Society, 28, (1974), 185-202.
- K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equation, 1st ed., Wiley, NJ, USA, (1993).
- I. Podlubny, Matrix approach to discrete fractional calculus, Fract Calc Appl Anal., 3 (4), (2000), 359-386.
- F.M. Atici and P.W. Eloe, Discrete fractional calculus with the nabla operator, Electron. J. Qual. Theory. Differ. Equ., 3, (2009), 1-12.
- F.M. Atici and N. Acar, Exponential functions of discrete fractional calculus, Appl. Anal. Discrete. Math., 7, (2013), 343-353.
- R. Yilmazer, M. Inc, F. Tchier and D. Baleanu, Particular solutions of the confluent hypergeometric differential equation by using the nabla fractional calculus operator, Entropy, 18 (2), (2016), 49.
- F.M. Atici and M. Uyanik, Analysis of discrete fractional operators, Appl. Anal. Discrete Math., 9 (1), (2015), 139-149.
Ayrıntılar
Birincil Dil
İngilizce
Konular
-
Bölüm
Araştırma Makalesi
Yazarlar
Okkes Ozturk
*
Türkiye
Yayımlanma Tarihi
31 Aralık 2016
Gönderilme Tarihi
14 Nisan 2016
Kabul Tarihi
7 Ekim 2016
Yayımlandığı Sayı
Yıl 2016 Cilt: 4 Sayı: 4