Asymptotic analysis of the Wright function with a large parameter

Ansari, Alireza; Argani, Hassan

doi:10.1016/j.jmaa.2021.125731

Cited by 8 publications

(1 citation statement)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

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.

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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.

View full text Add to dashboard Cite

show abstract

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

Askari,

Ansari

2024

Fract Calc Appl Anal

View full text Add to dashboard Cite

Wiener–Hopf technique for a fractional mixed boundary value problem in cylindrical layer

Ansari

Masomi

2023

Arab. J. Math.

View full text Add to dashboard Cite

In this paper, we study the heat transfer modeling during freezing of a biological tissue and present an analytical approach for solving the heat transfer problem in cryosurgery. We consider a time-fractional bio-heat equation in the cylindrical coordinate and employ the Wiener–Hopf technique to find the temperature of tissue in two different domains by the factorization of associated Wiener–Hopf kernel. We discuss the fundamental roles of the Bessel and Wright functions in determining the analytical solution of fractional cryosurgery problem.

show abstract

Asymptotic analysis of the Wright function with a large parameter

Cited by 8 publications

References 33 publications

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

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

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

Wiener–Hopf technique for a fractional mixed boundary value problem in cylindrical layer

Contact Info

Product

Resources

About