The discrete convolution for fractional cosine-sine series and its application in convolution equations

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...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 2; pp. 2641 - 2656
Main Authors Wang, Rongbo, Feng, Qiang, Ji, Jinyi
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
convolution equations
discrete convolution
fractional cosine series (frcs)
fractional sine series (frss)
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024130