Uyumlu Kesirli Bir Dalga Denklemi Üzerine

Abstract

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.

Keywords

• Uyumlu kesirli türev,Özdeğer,Özfonksiyon

On a Conformable Fractional Wave Equation

Abstract

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.

Keywords

• Conformable fractional derivative,Eigenvalue,Eigenfunction

References

1. [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. [2] Miller, K. S. 1993. An Introduction to Fractional Calculus and Fractional Differential Equations. J. Wiley and Sons, New York.
3. [3] Podlubny, I. 1999. Fractional Differential Equations. Academic Press, USA.
4. [4] Kilbas, A., Srivastava H., Trujillo J. 2006. Theory and Applications of Fractional Differential Equations, in:Math. Studies. North-Holland, New York.
5. [5] Schneider, W., Wyss, W. 1989. Fractional Diffusion and Wave Equations. J. Math. Phys., 30(1), 134-144.
6. [6] Kulish, V. V., Lage, J. L. 2002. Application of Fractional Calculus to Fluid Mechanics. J. Fluids Eng., 124(3), 803-806.
7. [7] Magin, R. L. 2010. Fractional Calculus Models of Complex Dynamics in Biological Tissues. Comput. Math. Appl., 59(5), 1586-1593.
8. [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. [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. [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. [11] Abu Hammad, M., Khalil, R. 2014. Conformable Fractional Heat Differential Equations. Internat. J. Pure. Appl. Math., 94(2), 215-221.
12. [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. [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. [14] Abdeljawad, T. 2015. On Conformable Fractional Calculus. Journal of Computational and Applied Mathematics, 27(9), 57-66.
15. [15] Anderson, D. R., Ulness, D. J. 2016. Results for Conformable Differential Equations. Preprint.
16. [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. [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. [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.