Operational Calculus for the Fractional Fourier-Laplace Transform

Vidya Sharma, Akash Patalwanshi

Abstract: In this paper, we introduce the Fractional Fourier-Laplace Transform (FrFLT), rigorously defining its structure, extending it to all fractional parameters. A comprehensive operational calculus for the FrFLT is developed by proving its core properties, including linearity, shifting, scaling, differentiation, and modulation. These properties describe how the FrFLT interacts with linear combinations of functions, spatial shifts, partial derivatives, scaling transformations, and harmonic modulations. Additionally, we analyze the behavior of the FrFLT for various parameter values, providing insights into its structure and operational utility. These results demonstrate the FrFLT?s versatility and potential for applications in signal processing, mathematical physics, and engineering. Furthermore, this research establishes a foundation for future exploration of the FrFLT in solving fractional differential equations and related problems.

Keywords: Fractional Fourier transform, Fractional Laplace transform, Fractional Fourier-Laplace transform, Signal processing

How to Cite?: Vidya Sharma, Akash Patalwanshi, "Operational Calculus for the Fractional Fourier-Laplace Transform", Volume 14 Issue 1, January 2025, International Journal of Science and Research (IJSR), Pages: 853-862, https://www.ijsr.net/getabstract.php?paperid=SR25119122327, DOI: https://dx.doi.org/10.21275/SR25119122327