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Uyumlu Kesirli Bir Dalga Denklemi Üzerine

Yıl 2018, Cilt: 22 Sayı: 3, 1110 - 1113, 20.09.2018
https://doi.org/10.19113/sdufenbed.430296

Öz

Çalışmada, uyumlu kesirli kısmi türevle ifade edilen bir dalga denklemine, genelleştirilmiş Fourier metodu uygulanarak elde edilen, uyumlu kesirli sınır değer probleminin özdeğer ve özfonksiyon özellikleri incelenmiştir.

Kaynakça

  • [1] Oldham, K. B., Spainer, J. 1974. The Fractional Calculus, Theory and Applications of Differentiation and Integration to Arbitrary Order. Vol. 111. Academic Press, New York.
  • [2] Miller, K. S. 1993. An Introduction to Fractional Calculus and Fractional Differential Equations. J. Wiley and Sons, New York.
  • [3] Podlubny, I. 1999. Fractional Differential Equations. Academic Press, USA.
  • [4] Kilbas, A., Srivastava H., Trujillo J. 2006. Theory and Applications of Fractional Differential Equations, in:Math. Studies. North-Holland, New York.
  • [5] Schneider, W., Wyss, W. 1989. Fractional Diffusion and Wave Equations. J. Math. Phys., 30(1), 134-144.
  • [6] Kulish, V. V., Lage, J. L. 2002. Application of Fractional Calculus to Fluid Mechanics. J. Fluids Eng., 124(3), 803-806.
  • [7] Magin, R. L. 2010. Fractional Calculus Models of Complex Dynamics in Biological Tissues. Comput. Math. Appl., 59(5), 1586-1593.
  • [8] Balachandran, K., Kiruthika, S., Rivero, M., Trujillo, J. J. 2012. Existence of Solutions for Fractional Delay Integrodifferential Equations. Journal of Applied Nonlinear Dynamics, 1, 309-319.
  • [9] Khalil, R., Horani, M. Al., Yousef, A., Sababheh, M. 2014. A New Definition of Fractional Derivative. Journal of Computational and Applied Mathematics, 264, 65-70.
  • [10] Abu Hammad, M., Khalil, R. 2014. Abel’s Formula and Wronskian for Conformable Fractional Differential Equations. Internat. J. Diff. Equ. Appl., 13(3), 177-183.
  • [11] Abu Hammad, M., Khalil, R. 2014. Conformable Fractional Heat Differential Equations. Internat. J. Pure. Appl. Math., 94(2), 215-221.
  • [12] Gokdogan, A., Unal, E., Celik, E. 2016. Existence and Uniqueness Theorems for Sequential Linear Conformable Fractional Differential Equations. Miskolc Mathematical Notes, 17(1), 267-279.
  • [13] Khalil, R., Abu-Shaab, H. 2015. Solution of Some Conformable Fractional Differential Equations. International Journal of Pure and Applied Mathematics, 103(4), 667-673.
  • [14] Abdeljawad, T. 2015. On Conformable Fractional Calculus. Journal of Computational and Applied Mathematics, 27(9), 57-66.
  • [15] Anderson, D. R., Ulness, D. J. 2016. Results for Conformable Differential Equations. Preprint.
  • [16] Anderson, D. R. 2017. Second-Order Self-Adjoint Differential Equations Using a Proportional-Derivative Controller. Commun. Appl. Nonlinear Anal., 24(1), 17-48.
  • [17] Gulsen, T., Yilmaz, E., Goktas, S. 2017. Conformable Fractional Dirac System on Time Scales. Journal of Inequalities and Applications, 2017(161), doi: 10.1186/s13660-017-1434-8.
  • [18] Gulsen, T., Yilmaz, E., Kemaloglu, H. 2018. Conformable Fractional Sturm-Liouville Equation and Some Existence Results on Time Scales. Turkish Journal of Mathematics, 42, 1348-1360.

On a Conformable Fractional Wave Equation

Yıl 2018, Cilt: 22 Sayı: 3, 1110 - 1113, 20.09.2018
https://doi.org/10.19113/sdufenbed.430296

Öz

This paper is devoted to examine the spectral properties of a  conformable boundary value problem which is obtained from a conformable wave equation by applying the generalized Fourier method.

Kaynakça

  • [1] Oldham, K. B., Spainer, J. 1974. The Fractional Calculus, Theory and Applications of Differentiation and Integration to Arbitrary Order. Vol. 111. Academic Press, New York.
  • [2] Miller, K. S. 1993. An Introduction to Fractional Calculus and Fractional Differential Equations. J. Wiley and Sons, New York.
  • [3] Podlubny, I. 1999. Fractional Differential Equations. Academic Press, USA.
  • [4] Kilbas, A., Srivastava H., Trujillo J. 2006. Theory and Applications of Fractional Differential Equations, in:Math. Studies. North-Holland, New York.
  • [5] Schneider, W., Wyss, W. 1989. Fractional Diffusion and Wave Equations. J. Math. Phys., 30(1), 134-144.
  • [6] Kulish, V. V., Lage, J. L. 2002. Application of Fractional Calculus to Fluid Mechanics. J. Fluids Eng., 124(3), 803-806.
  • [7] Magin, R. L. 2010. Fractional Calculus Models of Complex Dynamics in Biological Tissues. Comput. Math. Appl., 59(5), 1586-1593.
  • [8] Balachandran, K., Kiruthika, S., Rivero, M., Trujillo, J. J. 2012. Existence of Solutions for Fractional Delay Integrodifferential Equations. Journal of Applied Nonlinear Dynamics, 1, 309-319.
  • [9] Khalil, R., Horani, M. Al., Yousef, A., Sababheh, M. 2014. A New Definition of Fractional Derivative. Journal of Computational and Applied Mathematics, 264, 65-70.
  • [10] Abu Hammad, M., Khalil, R. 2014. Abel’s Formula and Wronskian for Conformable Fractional Differential Equations. Internat. J. Diff. Equ. Appl., 13(3), 177-183.
  • [11] Abu Hammad, M., Khalil, R. 2014. Conformable Fractional Heat Differential Equations. Internat. J. Pure. Appl. Math., 94(2), 215-221.
  • [12] Gokdogan, A., Unal, E., Celik, E. 2016. Existence and Uniqueness Theorems for Sequential Linear Conformable Fractional Differential Equations. Miskolc Mathematical Notes, 17(1), 267-279.
  • [13] Khalil, R., Abu-Shaab, H. 2015. Solution of Some Conformable Fractional Differential Equations. International Journal of Pure and Applied Mathematics, 103(4), 667-673.
  • [14] Abdeljawad, T. 2015. On Conformable Fractional Calculus. Journal of Computational and Applied Mathematics, 27(9), 57-66.
  • [15] Anderson, D. R., Ulness, D. J. 2016. Results for Conformable Differential Equations. Preprint.
  • [16] Anderson, D. R. 2017. Second-Order Self-Adjoint Differential Equations Using a Proportional-Derivative Controller. Commun. Appl. Nonlinear Anal., 24(1), 17-48.
  • [17] Gulsen, T., Yilmaz, E., Goktas, S. 2017. Conformable Fractional Dirac System on Time Scales. Journal of Inequalities and Applications, 2017(161), doi: 10.1186/s13660-017-1434-8.
  • [18] Gulsen, T., Yilmaz, E., Kemaloglu, H. 2018. Conformable Fractional Sturm-Liouville Equation and Some Existence Results on Time Scales. Turkish Journal of Mathematics, 42, 1348-1360.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Fatma Ayça Çetinkaya

Yayımlanma Tarihi 20 Eylül 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 22 Sayı: 3

Kaynak Göster

APA Çetinkaya, F. A. (2018). Uyumlu Kesirli Bir Dalga Denklemi Üzerine. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(3), 1110-1113. https://doi.org/10.19113/sdufenbed.430296
AMA Çetinkaya FA. Uyumlu Kesirli Bir Dalga Denklemi Üzerine. SDÜ Fen Bil Enst Der. Eylül 2018;22(3):1110-1113. doi:10.19113/sdufenbed.430296
Chicago Çetinkaya, Fatma Ayça. “Uyumlu Kesirli Bir Dalga Denklemi Üzerine”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, sy. 3 (Eylül 2018): 1110-13. https://doi.org/10.19113/sdufenbed.430296.
EndNote Çetinkaya FA (01 Eylül 2018) Uyumlu Kesirli Bir Dalga Denklemi Üzerine. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 3 1110–1113.
IEEE F. A. Çetinkaya, “Uyumlu Kesirli Bir Dalga Denklemi Üzerine”, SDÜ Fen Bil Enst Der, c. 22, sy. 3, ss. 1110–1113, 2018, doi: 10.19113/sdufenbed.430296.
ISNAD Çetinkaya, Fatma Ayça. “Uyumlu Kesirli Bir Dalga Denklemi Üzerine”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/3 (Eylül 2018), 1110-1113. https://doi.org/10.19113/sdufenbed.430296.
JAMA Çetinkaya FA. Uyumlu Kesirli Bir Dalga Denklemi Üzerine. SDÜ Fen Bil Enst Der. 2018;22:1110–1113.
MLA Çetinkaya, Fatma Ayça. “Uyumlu Kesirli Bir Dalga Denklemi Üzerine”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 22, sy. 3, 2018, ss. 1110-3, doi:10.19113/sdufenbed.430296.
Vancouver Çetinkaya FA. Uyumlu Kesirli Bir Dalga Denklemi Üzerine. SDÜ Fen Bil Enst Der. 2018;22(3):1110-3.

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