Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator

Askari, Hassan; Ansari, Alireza

doi:10.1007/s13540-024-00263-7

Cited by 1 publication

(2 citation statements)

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“…and differentiate from the both sides of (2.22) with respect to δ, and then put δ = 1 (see [10] for the asymptotic analysis of this function with large parameters). In this respect, we get…”

Section: Fractional Momentmentioning

confidence: 99%

“…We use a logarithmic map for the well-known Hankel contour and construct the Schläfli contour to orient our study. The Schläfli contour integration have been recently used for analyzing the asymptotic expansions of some special functions [5,10,32], and it is our main contour for analyzing the asymptotic expansion of the Volterra-Bessel function.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic analysis of fundamental solution of multi-dimensional distributed-order time-fractional diffusion equation with unit density function

Hashemzadeh Kalvari,

Ansari,

Askari

2024

J. Phys. A: Math. Theor.

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In this paper, we consider the multi-dimensional distributed-order time-fractional diffusion equation with the unit density function. We introduce the new Volterra-Bessel function and give the integral representations of fundamental solutions of equations in terms of this function in the whole- and half-space. The fractional moments of fundamental solutions are also provided in the higher dimensions using the Mellin transforms. We further apply steepest descent method to find the asymptotic behaviors of solutions using the Schl"{a}fli integral of the Volterra-Bessel function. In this respect, we study the asymptotic analysis of the Volterra-Bessel function with the large parameters, and subsequently obtain the asymptotic behaviors of fundamental solutions with a discussion on the large space variable, large time variable, higher dimensions and small diffusivity constant.

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Section: Fractional Momentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%