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METHOD OF VARIATION OF PARAMETERS FOR THE THIRD-ORDER LINEAR PROPORTIONAL DYNAMIC EQUATIONS

Cilt: 6 Sayı: 2 31 Aralık 2023
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METHOD OF VARIATION OF PARAMETERS FOR THE THIRD-ORDER LINEAR PROPORTIONAL DYNAMIC EQUATIONS

Öz

The differentiation and integration of an integer order are known as fractional calculus. It is possible to think of the proportional derivative as a generalization of a congruent fractional derivative, which is one of the types of fractional calculus. In this article, utilizing the proportional derivative and its characteristics on the time scale, the method of variation of parameters for the third-order linear nonhomogeneous differential equations is given. Then, an example is provided to illustrate how to apply the provided approach.

Anahtar Kelimeler

Teşekkür

This research is part of the second author’s master’s thesis, which is carried out at Firat University, Türkiye.

Kaynakça

  1. 1. Abdeljewad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279, 57–66.
  2. 2. Agarwal, R., Bohner, M., O'Regan, D. & Peterson, A. (2002). Dynamic equations on time scales: a survey. Journal of Computational and Applied Mathematics, 141(1-2), 1-26.
  3. 3. Anderson, D.R. & Georgiev, S.G. (2020). Conformable Dynamic Equations on Time Scales. Chapman and Hall/CRC.
  4. 4. Anderson, D.R. & Ulness, D.J. (2015). Newly defined conformable derivatives. Advances in Dynamical Systems and Applications, 10(2), 109-137.
  5. 5. Aulbach, B. & Hilger. S. (1990). A unified approach to continuous and discrete Dynamics. in: Qualitative Theory of Differential Equations (Szeged, 1988), 37–56, Colloq. Math. Soc. János Bolyai, 53 North-Holland, Amsterdam.
  6. 6. Benkhettou, N., Brito da Cruz, A. M. C. & Torres, D. F. M. (2015). A fractional calculus on arbitrary time scales: Fractional differentiation and fractional integration. Signal Processing, 107, 230– 237.
  7. 7. Benkhettou, N., Hassani, S. & Torres, D. F. M. (2016). A conformable fractional calculus on arbitrary time scales. Journal of King Saud University (Science), 28(1), 93-98.
  8. 8. Bohner, M. & Peterson, A. (2001). Dynamic equations on time scales, An introduction with applications. Boston, MA: Birkhauser.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Yazılım Mühendisliği (Diğer)

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

31 Aralık 2023

Gönderilme Tarihi

5 Temmuz 2023

Kabul Tarihi

4 Eylül 2023

Yayımlandığı Sayı

Yıl 2023 Cilt: 6 Sayı: 2

Kaynak Göster

APA
Gülşen, T., & Acar, M. (2023). METHOD OF VARIATION OF PARAMETERS FOR THE THIRD-ORDER LINEAR PROPORTIONAL DYNAMIC EQUATIONS. Bartın University International Journal of Natural and Applied Sciences, 6(2), 135-144. https://doi.org/10.55930/jonas.1321901
AMA
1.Gülşen T, Acar M. METHOD OF VARIATION OF PARAMETERS FOR THE THIRD-ORDER LINEAR PROPORTIONAL DYNAMIC EQUATIONS. JONAS. 2023;6(2):135-144. doi:10.55930/jonas.1321901
Chicago
Gülşen, Tuba, ve Mehmet Acar. 2023. “METHOD OF VARIATION OF PARAMETERS FOR THE THIRD-ORDER LINEAR PROPORTIONAL DYNAMIC EQUATIONS”. Bartın University International Journal of Natural and Applied Sciences 6 (2): 135-44. https://doi.org/10.55930/jonas.1321901.
EndNote
Gülşen T, Acar M (01 Aralık 2023) METHOD OF VARIATION OF PARAMETERS FOR THE THIRD-ORDER LINEAR PROPORTIONAL DYNAMIC EQUATIONS. Bartın University International Journal of Natural and Applied Sciences 6 2 135–144.
IEEE
[1]T. Gülşen ve M. Acar, “METHOD OF VARIATION OF PARAMETERS FOR THE THIRD-ORDER LINEAR PROPORTIONAL DYNAMIC EQUATIONS”, JONAS, c. 6, sy 2, ss. 135–144, Ara. 2023, doi: 10.55930/jonas.1321901.
ISNAD
Gülşen, Tuba - Acar, Mehmet. “METHOD OF VARIATION OF PARAMETERS FOR THE THIRD-ORDER LINEAR PROPORTIONAL DYNAMIC EQUATIONS”. Bartın University International Journal of Natural and Applied Sciences 6/2 (01 Aralık 2023): 135-144. https://doi.org/10.55930/jonas.1321901.
JAMA
1.Gülşen T, Acar M. METHOD OF VARIATION OF PARAMETERS FOR THE THIRD-ORDER LINEAR PROPORTIONAL DYNAMIC EQUATIONS. JONAS. 2023;6:135–144.
MLA
Gülşen, Tuba, ve Mehmet Acar. “METHOD OF VARIATION OF PARAMETERS FOR THE THIRD-ORDER LINEAR PROPORTIONAL DYNAMIC EQUATIONS”. Bartın University International Journal of Natural and Applied Sciences, c. 6, sy 2, Aralık 2023, ss. 135-44, doi:10.55930/jonas.1321901.
Vancouver
1.Tuba Gülşen, Mehmet Acar. METHOD OF VARIATION OF PARAMETERS FOR THE THIRD-ORDER LINEAR PROPORTIONAL DYNAMIC EQUATIONS. JONAS. 01 Aralık 2023;6(2):135-44. doi:10.55930/jonas.1321901