Uyumlu Kesir Mertebeden Chebyshev Diferensiyel Denklemleri ve Kesirsel Chebyshev Polinomları

Bu çalışmada, = 0 - 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.

Conformable Fractional Chebyshev Equations and Fractional Chebyshev Polynomials

In this work, we give the fractional power series solutions around = 0 -ordinary point of conformable fractional first and second kind Chebyshev differential equations. We present first and second kind fractional Chebyshev polynomials using by these solutions. Finally, we present certain property of fractional first and second kind Chebyshev polynomials.

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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 Conformable Fractional Differential Equations, to appear, Miskolc Mathematical Notes.
Gökdoğan, A., Ünal, E. and Çelik, E., 2015. Conformable Fractional Functions, arXiv preprint arXiv:1506.07382. Equation and Bessel
Ünal, E., Gökdoğan, A. and Çelik, E., 2015. Solutions of Sequential Conformable Fractional Differential Equations Conformable Equation, British Journal of Applied Science & Technology, 10(2), 1-11. Ordinary Hermite Differential Fractional