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<p>In this paper, we develop the optimal parabolic/hyperbolic contour method for computing the inverse Laplace transform of Volterra-Bessel function. A comparative analysis is given for the errors of methods and the convergence rates. The results show the convergence rate of hyperbolic contour is faster than that of the parabolic contour. We also concentrate on the asymptotic behavior of the Tricomi confluent hypergeometric function and establish different cases for the convergence analysis. We finally introduce the fractional Volterra-Bessel integral/derivative and investigate fractional relaxation equation involving this type of generalized fractional operator.</p>

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A comparative analysis for computation of the Volterra-Bessel function using the optimal parabolic and hyperbolic contours: application to fractional relaxation equation

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • Arman Hashemzadeh Kalvari,
  • Alireza Ansari,
  • Hassan Askari

摘要

In this paper, we develop the optimal parabolic/hyperbolic contour method for computing the inverse Laplace transform of Volterra-Bessel function. A comparative analysis is given for the errors of methods and the convergence rates. The results show the convergence rate of hyperbolic contour is faster than that of the parabolic contour. We also concentrate on the asymptotic behavior of the Tricomi confluent hypergeometric function and establish different cases for the convergence analysis. We finally introduce the fractional Volterra-Bessel integral/derivative and investigate fractional relaxation equation involving this type of generalized fractional operator.