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

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...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2024-06, Vol.57 (24), p.245202
Main Authors: Hashemzadeh Kalvari, Arman, Ansari, Alireza, Askari, Hassan
Format: Article
Language:English
Subjects:
asymptotic analysis
Laplace transform
time-fractional diffusion equation
Volterra–Bessel function
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Summary: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 Schläfli 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.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ad4ca9