Time-fractional telegraph equation of distributed order in higher dimensions

Vieira, N.; Rodrigues, M. M.; Ferreira, Milton

doi:10.1016/j.cnsns.2021.105925

Cited by 20 publications

(13 citation statements)

References 27 publications

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“…Here, we intend to represent the fractional moment of the fundamental solution of (1.1) in the Laplace domain. Let us start with the relation (1.4) and follow the approach of [6,50] for defining the fractional moment by the Mellin transform of ū(|x n |, s) as…”

Section: Fractional Momentmentioning

confidence: 99%

“…is a modification of sub-diffusion and has attracted a lot attention by many researchers in the last two decades. In the literature, this equation relates to the initial works [13,14,[20][21][22][23][24], and provides new mathematical and theoretical aspects for studying of the physical and natural sciences in different cases of b(σ) and fractional operators using the analytical and numerical methods [6,8,9,18,25,27,34,35,44,45,47,49,50].…”

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%

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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“…Let us calculate the Mellin transforms that appear in (48). The Mellin transform of h 2 was already calculated in [49] (see Formula ( 43)):…”

Section: Solution In the Space-time Domainmentioning

confidence: 99%

Time-fractional telegraph equation with ψ-Hilfer derivatives

Vieira

Ferreira

Rodrigues

2022

Chaos, Solitons & Fractals

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“…The DOTFTE can be associated with super/subdiffusive processes for specific density function choices. Vieira et al [25] presented the fundamental solution of the DOTFTE in the n-dimensional space by using Fox H-functions via a combination of the Mellin, Fourier and Laplace transforms. Also, the provided techniques are generalisation of approaches for DOTFDWE that have been employed by numerous authors (see [26,27]).…”

Section: Introductionmentioning

confidence: 99%

Improved Gegenbauer spectral tau algorithms for distributed-order time-fractional telegraph models in multi-dimensions

Ahmed

Hashem

2023

Numer Algor

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The distributed-order fractional telegraph models are commonly used to describe the phenomenas of diffusion and wave-like anomalous, which can model processes without a power-law scale across the entire temporal domain. To increase the range of implementation of distributed-order fractional telegraph models, there is a need to present effective and accurate numerical algorithms to solve these models, as these models are hard to solve analytically. In this work, a novel matrix representation of the distributed-order fractional derivative based on shifted Gegenbauer (SG) polynomials has been derived. Also, two efficient algorithms based on the aforementioned operatonal matrix and the spectral tau method have been constructed for solving the one- and two-dimensional (1D and 2D) distributed-order time-fractional telegraph models with spatial variable coefficients. Also, a new operational matrix of the multiplication of space vectors has been built to have the ability in applying the tau method in the 2D case. The convergence and error bound analysis of the presented techniques are investigated. Moreover, the presented algorithms are applied on four miscellaneous test examples to illustrate the robustness and effectiveness of these algorithms.

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Time-fractional telegraph equation of distributed order in higher dimensions

Cited by 20 publications

References 27 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

Time-fractional telegraph equation with ψ-Hilfer derivatives

Improved Gegenbauer spectral tau algorithms for distributed-order time-fractional telegraph models in multi-dimensions

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