Araştırma Makalesi

A study on nabla discrete fractional operator in mass - spring - damper system

Cilt: 4 Sayı: 4 31 Aralık 2016
PDF İndir
EN

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

  1. K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press Cambridge, MA, USA (1974).
  2. J.B. Diaz and T.J. Osler, Differences of fractional order, American Mathematical Society, 28, (1974), 185-202.
  3. K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equation, 1st ed., Wiley, NJ, USA, (1993).
  4. I. Podlubny, Matrix approach to discrete fractional calculus, Fract Calc Appl Anal., 3 (4), (2000), 359-386.
  5. F.M. Atici and P.W. Eloe, Discrete fractional calculus with the nabla operator, Electron. J. Qual. Theory. Differ. Equ., 3, (2009), 1-12.
  6. F.M. Atici and N. Acar, Exponential functions of discrete fractional calculus, Appl. Anal. Discrete. Math., 7, (2013), 343-353.
  7. 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.
  8. 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

Yayımlanma Tarihi

31 Aralık 2016

Gönderilme Tarihi

14 Nisan 2016

Kabul Tarihi

7 Ekim 2016

Yayımlandığı Sayı

Yıl 2016 Cilt: 4 Sayı: 4

Kaynak Göster

APA
Ozturk, O. (2016). A study on nabla discrete fractional operator in mass - spring - damper system. New Trends in Mathematical Sciences, 4(4), 137-144. https://izlik.org/JA66UG56JG
AMA
1.Ozturk O. A study on nabla discrete fractional operator in mass - spring - damper system. New Trends in Mathematical Sciences. 2016;4(4):137-144. https://izlik.org/JA66UG56JG
Chicago
Ozturk, Okkes. 2016. “A study on nabla discrete fractional operator in mass - spring - damper system”. New Trends in Mathematical Sciences 4 (4): 137-44. https://izlik.org/JA66UG56JG.
EndNote
Ozturk O (01 Aralık 2016) A study on nabla discrete fractional operator in mass - spring - damper system. New Trends in Mathematical Sciences 4 4 137–144.
IEEE
[1]O. Ozturk, “A study on nabla discrete fractional operator in mass - spring - damper system”, New Trends in Mathematical Sciences, c. 4, sy 4, ss. 137–144, Ara. 2016, [çevrimiçi]. Erişim adresi: https://izlik.org/JA66UG56JG
ISNAD
Ozturk, Okkes. “A study on nabla discrete fractional operator in mass - spring - damper system”. New Trends in Mathematical Sciences 4/4 (01 Aralık 2016): 137-144. https://izlik.org/JA66UG56JG.
JAMA
1.Ozturk O. A study on nabla discrete fractional operator in mass - spring - damper system. New Trends in Mathematical Sciences. 2016;4:137–144.
MLA
Ozturk, Okkes. “A study on nabla discrete fractional operator in mass - spring - damper system”. New Trends in Mathematical Sciences, c. 4, sy 4, Aralık 2016, ss. 137-44, https://izlik.org/JA66UG56JG.
Vancouver
1.Okkes Ozturk. A study on nabla discrete fractional operator in mass - spring - damper system. New Trends in Mathematical Sciences [Internet]. 01 Aralık 2016;4(4):137-44. Erişim adresi: https://izlik.org/JA66UG56JG