Application of DGJ method for solving non-linear local fractional heat equations

In the current investigation, the thermoelasticity with a model of fractional order is used to discuss a problem of thermoelastic half‐space. Such theory depends on the time‐fractional derivative of Caputo of order α. The thermal conductivity is considered to be a variable, and the medium surface is subjected to a free from traction and a thermal shock. Then, the transform of Laplace has been utilized for the solutions of the governing equations. The inverse of the Laplace transform entertained numerically, employing a technique based on methods of Fourier expansion. The obtained numerical solutions for different variables and the obtained results are offered graphically. The effect of the variation of thermal conductivity as well as a fractional‐order parameter on displacement, temperature, and stress are studied. A comparison is made between the results obtained in the current investigation and the previous results by others when the new parameters neglect. The results obtained indicated to the significant role of the heat conduction fractional model, thermal conductivity, temperature dependent, and thermal relaxation time on the thermoelastic half‐space.

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Fractional heat conduction model with phase lags for a half‐space with thermal conductivity and temperature dependent

Abo‐Dahab

Abouelregal

Ahmad

2020

Math Methods in App Sciences

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Application of DGJ method for solving non-linear local fractional heat equations

Abstract: In this paper, the initial value problem for a new non-linear local fractional heat equation is considered. The fractional complex transform method and the DGJ decomposition method are used to solve the problem, and the approximate analytical solutions are also obtained.

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Fractional heat conduction model with phase lags for a half‐space with thermal conductivity and temperature dependent

Fractional heat conduction model with phase lags for a half‐space with thermal conductivity and temperature dependent

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