Matrix-based evaluation of the fractional Hankel transform by bessel series expansion

Magdy Tawfik Hanna

Applied Mathematics and Computation, 2026, vol. 509, issue C

Abstract: The main problem in the fractional Hankel transform (FRHT) application is the difficulty encountered in any attempt toward the analytical evaluation of the integral appearing in its definition. A matrix-based numerical evaluation technique is contributed and obtained using a truncated Fourier-Bessel series expansion of a space-limited signal. The algorithm for implementing the contributed method involves only matrix computation, thus avoiding numerical integration with its associated problems of instability and inaccuracy. An expression is derived for the fractional Hankel transform of a generalized Gaussian signal, making it possible to assess the contributed numerical technique by comparing the numerically evaluated fractional transform with samples of the derived expression of the FRHT. The simulation results demonstrate the high accuracy of the contributed numerical evaluation method.

Keywords: Fourier-Bessel series; Hypergeometric function; Hankel transform (HT); Fractional transform; Matrix-based numerical evaluation; Generalized Gaussian signal (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:509:y:2026:i:c:s0096300325003972

DOI: 10.1016/j.amc.2025.129671

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