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Some closed form series solutions for the time-fractional diffusion-wave equation in polar coordinates with a generalized Caputo fractional derivative

Elkott Ibrahim, Abdel-Latif Mohamed S., El-Kalla Ibrahim L., Abdel Kader Abass H.

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 2

5--14

EN

In this paper, we obtain some closed form series solutions for the time fractional diffusion-wave equation (TFDWE) with the generalized time-fractional Caputo derivative (GTFCD) associated with a source term in polar coordinates. These solutions are found using generalized Laplace and Hankel transforms. We obtained the closed form series solutions in the form of the Polygamma function. The effect of the fractional order derivative on the diffusion-wave variable is illustrated graphically.

2

Analytical solution of a fractional model of fluid flow through narrowing system in terms of Mittag-Leffler function

Choudhary A., Kumar D., Singh J.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 1

1--11

EN

In this work, we discuss a fractional model of a flow equation in a simple pipeline. Pipeline narrowing is a crucial aspect in drinking water distribution processes, sewage system and in oil-well schemes. The solution of the mathematical model is determined with the aid of the Sumudu transform and finite Hankel transform. The results derived in the current study are in compact and graceful forms in terms of the Mittag-Leffler type function, which are convenient for numerical and theoretical evaluation.

3

A two dimensional axisymmetric thermoelastic diffusion problem of micropolar porous circular plate with dual phase lag model

Kumar R., Miglani A., Rani R.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 4

1389--1406

EN

In the present work, we consider a two dimensional axisymmetric problem of micropolar porous circular plate with thermal and chemical potential sources in the context of the theory of dual phase lag generalized thermoelastic diffusion. The potential functions are used to analyze the problem. The Laplace and Hankel transforms techniques are used to find the expressions of displacements, microrotation, volume fraction field, temperature distribution, concentration and stresses in the transformed domain. The inversion of transforms based on Fourier expansion techniques is applied to obtain the results in the physical domain. The numerical results for resulting quantities are obtained and depicted graphically. Effect of porosity, LS theory and phase lag are presented on the resulting quantities. Some particular cases are also deduced.

4

Axisymmetric vibration for micropolar porous thermoelastic circular plate

Kumar R., Kaushal P., Sharma R.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 3

583--600

EN

The present investigation is concerned with a two dimensional axisymmetric problem in a homogeneous isotropic micropolar porous thermoelastic circular plate by using the eigen value approach. The Laplace and Hankel transform are used to solve the problem. The expression of displacements, microrotation, volume fraction field, temperature distribution and stresses are obtained in the transformed domain subjected to thermomechanical sources. A computer algorithm is developed for numerical computations. To obtain the resulting quantities in a physical domain, a numerical inversion technique is used. The resulting quantities are depicted graphically for a specific model. Some special cases are also deduced.

5

Analysis of fundamental solutions to fractional diffusion-wave equation in polar coordinates

Povstenko Y.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2009

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Vol. 14

97-104

EN

The diffusion-wave equation is a mathematical model of a wide range of important physical phenomena. The first and second Cauchy problems and the source problem for the diffusion-wave equation are considered in cylindrical coordinates. The Caputo fractional derivative is used. The Laplace and Hankel transforms are employed. The results are illustrated graphically.

6

Torsional oscillation of rigid disk in an infinite cylinder

Manna S. K., Gosh S., Mandal S. C.

Journal of Technical Physics

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2003

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Vol. 44, no 4

341-347

EN

In this paper torsional oscillation of rigid disk in an infinite cylinder has been analyzed. The problem is reduced to solve the Fredholm integral equation of second kind by applying Hankel and Fourier transforms. Stress intensity factor at the edge of the strip has been derived and plotted to show the effect of cylinder width on stress intensity factor.