Author:
Wang Rongbo,Feng Qiang,Ji Jinyi
Abstract
<abstract><p>The fractional sine series (FRSS) and the fractional cosine series (FRCS) were defined. Three types of discrete convolution operations for FRCS and FRSS were introduced, along with a detailed investigation into their corresponding convolution theorems. The interrelationship between these convolution operations was also discussed. Additionally, as an application of the presented results, two forms of discrete convolution equations based on the proposed convolution theorems were examined, resulting in explicit solutions for these equations. Furthermore, numerical simulations were provided to demonstrate that our proposed solution can be easily implemented with low computational complexity.</p>
</abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference34 articles.
1. I. E. Lager, M. Štumpf, G. A. E. Vandenbosch, G. Antonini, Evaluation of convolution integrals at late-times revisited, IEEE Trans. Antennas Propag., 70 (2022), 9953–9958. https://doi.org/10.1109/TAP.2022.3168347
2. L. Liu, J. J. Ma, Collocation boundary value methods for auto-convolution Volterra integral equations, Appl. Numer. Math., 177 (2022), 1–17. https://doi.org/10.1016/j.apnum.2022.03.004
3. Y. Xiang, S. Yuan, Q. Feng, Fractional Fourier cosine and sine Laplace weighted convolution and its application, IET Signal Process., 17 (2023), 12170. https://doi.org/10.1049/sil2.12170
4. M. L. Maslakov, New approach to the iterative method for numerical solution of a convolution type equation determined for a certain class of problems, Comput. Math. Math. Phys., 61 (2021), 1260–1268. https://doi.org/10.1134/S0965542521080054
5. M. S. Gao, J. Yu, Z. F. Yang, J. B. Zhao, Physics embedded graph convolution neural network for power flow calculation considering uncertain injections and topology, IEEE Trans. Neural Networks Learn. Syst., 2023. https://doi.org/10.1109/TNNLS.2023.3287028