Öz
Bu çalışmada, 𝑥=0 𝛼- adi noktası civarında uyumlu kesir mertebeden birinci ve ikinci tip Chebyshev Diferensiyel denklemlerin kesirsel seri çözümlerini verdik. Bu çözümlerden yararlanarak birinci ve ikinci tip kesirsel Chebyshev polinomlarını ifade ettik. Son olarak, elde edilen bu kesirsel Chebysev polinomların bazı özelliklerini sunduk
Anahtar Kelimeler
Uyumlu Kesir Merteben Diferensiyel Denklemler Uyumlu Kesir Merteben Chebyshev Diferensiyel Denklemleri Kesirsel Chebyshev Polinomları
Kaynakça
- Bayın, Ş. S., 2004. Fen ve Mühendislik Bilimlerinde Matematik Yöntemler, Ders Kitapları A.Ş.
- Kilbas, A., Srivastava, H. and Trujillo, J., 2006. Theory and Applications of Fractional Differential Equations, North-Holland, New York.
- Miller, K.S., 1993. An Introduction to Fractional Calculus and Fractional Differential Equations, J. Wiley and Sons, New York.
- Podlubny, I., 1999. Fractional Differential Equations, Academic Press, USA.
- Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M., 2014. A new Definition of Fractional Derivative, J. Comput. Appl. Math., 264, 65-70.
- Abdeljawad, T., 2015. On conformable fractional calculus, J. Comput. Appl. Math., 279, 57-66.
- Khalil, R., 2014. Fractional Fourier Series with Applications, American Journal of Computational and Applied Mathematics, 4.6, 187-191.
- Khalil, R. and Abu Hammad, M., 2014. Legendre fractional differential equation and Legendre fractional polynomials, International Journal of Applied Mathematical Research, 3.3, 214-219.
- Gökdoğan, A., Ünal, E. and Çelik, E., 2016. Existence and Uniqueness Theorems for Sequential Linear Conformable Fractional Differential Equations, to appear, Miskolc Mathematical Notes.
- Gökdoğan, A., Ünal, E. and Çelik, E., 2015. Conformable Fractional Bessel Equation and Bessel Functions, arXiv preprint arXiv:1506.07382.
- Ünal, E., Gökdoğan, A. and Çelik, E., 2015. Solutions of Sequential Conformable Fractional Differential Equations around an Ordinary Point and Conformable Fractional Hermite Differential Equation, British Journal of Applied Science & Technology, 10(2), 1-11.
Öz
Kaynakça
- Bayın, Ş. S., 2004. Fen ve Mühendislik Bilimlerinde Matematik Yöntemler, Ders Kitapları A.Ş.
- Kilbas, A., Srivastava, H. and Trujillo, J., 2006. Theory and Applications of Fractional Differential Equations, North-Holland, New York.
- Miller, K.S., 1993. An Introduction to Fractional Calculus and Fractional Differential Equations, J. Wiley and Sons, New York.
- Podlubny, I., 1999. Fractional Differential Equations, Academic Press, USA.
- Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M., 2014. A new Definition of Fractional Derivative, J. Comput. Appl. Math., 264, 65-70.
- Abdeljawad, T., 2015. On conformable fractional calculus, J. Comput. Appl. Math., 279, 57-66.
- Khalil, R., 2014. Fractional Fourier Series with Applications, American Journal of Computational and Applied Mathematics, 4.6, 187-191.
- Khalil, R. and Abu Hammad, M., 2014. Legendre fractional differential equation and Legendre fractional polynomials, International Journal of Applied Mathematical Research, 3.3, 214-219.
- Gökdoğan, A., Ünal, E. and Çelik, E., 2016. Existence and Uniqueness Theorems for Sequential Linear Conformable Fractional Differential Equations, to appear, Miskolc Mathematical Notes.
- Gökdoğan, A., Ünal, E. and Çelik, E., 2015. Conformable Fractional Bessel Equation and Bessel Functions, arXiv preprint arXiv:1506.07382.
- Ünal, E., Gökdoğan, A. and Çelik, E., 2015. Solutions of Sequential Conformable Fractional Differential Equations around an Ordinary Point and Conformable Fractional Hermite Differential Equation, British Journal of Applied Science & Technology, 10(2), 1-11.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2016 |
| Gönderilme Tarihi | 10 Nisan 2016 |
| Yayımlandığı Sayı | Yıl 2016 Cilt: 16 Sayı: 3 |