Geodesic
Qualitative analysis of Caputo fractional delayed difference system: a novel delayed discrete fractional sine and cosine-type function
Mahmudov, N. I. 1 ; Aydin, M.2
1 Department of Mathematics, Eastern Mediterranean University, Famagusta 99628 T. R. Northern Cyprus, Mersin 10, Turkey;Research Center of Econophysics, Azerbaijan State University of Economics (UNEC), Istiqlaliyyat Str. 6, Baku 1001, Azerbaijan
2 Department of Medical Services and Techniques, Muradiye Vocational School, Van Yuzuncu Yil University, Van, Turkey
Journal of nonlinear sciences and its applications, Tome 18 (2025) no. 1, p. 43-63.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we provide an explicit solution for the homogeneous fractional delay oscillation difference equation with an order $2{\delta}$ ranging from 1 to 2. This solution is achieved through the construction of discrete sine and cosine-type delayed matrix functions. Subsequently, we employ the discrete Laplace transform technique, a powerful method for handling nonhomogeneous terms, to investigate the solution of the corresponding nonhomogeneous equation. The study then delves into the Ulam-Hyers-type stabilities of the homogeneous equation, leveraging the representation of the solution. To validate the stability theory, we illustrate a numerical example. Finally, we extend our analysis by presenting an exact solution for the nonhomogeneous fractional difference equation with $12{\delta}2$, utilizing the discrete two-parameter delayed sine and cosine-type function.
DOI : 10.22436/jnsa.018.01.05
Classification : 33E12, 34Kxx, 39Axx, 39A06, 44A55
Keywords: Linear system, fractional difference, time-delay, nabla sine cosine, discrete delayed perturbation

Mahmudov, N. I.  1 ; Aydin, M. 2

1 Department of Mathematics, Eastern Mediterranean University, Famagusta 99628 T. R. Northern Cyprus, Mersin 10, Turkey;Research Center of Econophysics, Azerbaijan State University of Economics (UNEC), Istiqlaliyyat Str. 6, Baku 1001, Azerbaijan
2 Department of Medical Services and Techniques, Muradiye Vocational School, Van Yuzuncu Yil University, Van, Turkey 
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Mahmudov, N. I. ; Aydin, M. Qualitative analysis of Caputo fractional delayed difference system: a novel delayed discrete fractional sine and cosine-type function. Journal of nonlinear sciences and its applications, Tome 18 (2025) no. 1, p. 43-63. doi : 10.22436/jnsa.018.01.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.018.01.05/

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