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In this paper, we develop an accurate and efficient natural transform homotopy perturbation method for obtaining the numerical solution of nonlinear fractional Newell-Whitehead-Segel equation arise in various physical phenomena such as fluid mechanics, solid-state physics, optics, plasma physics, dispersion and chemical kinetics. We apply natural transform coupled with the homotopy perturbation method to bring down the nonlinear terms for obtaining the approximate solution. The innovation of the present approach illustrates some extensions and improvements of various results that were obtained previously. The authors show that the suggested approach is much easy to implement and capable to obtain the numerical solution of the nonlinear problems. Moreover, it is observed that, with the increase of more iterations, the suggested approach efficiency increases too. The solution graphs for each problem show that this method has a good agreement with the exact solution of the problem. [ABSTRACT FROM AUTHOR]

Moore-Gibson-Thompson (MGT) is an equation which appropriately describes the spread of sound waves in gasses and fluids as well as thermal/mechanical waves in elastic bodies. The objective of this article is to theoretically analyze the generalized thermoelasticity models that have been presented as the development of the Fourier's law dealing with the paradox of unlimited propagation velocities of thermal waves. For this purpose, a new model is presented which combines the third type of Green and Naghdi model (GN-III) with the generalized theory including the relaxation time based on the MGT equation. The proposed model may be considered as a generalization of previous thermoelastic theories. To examine the introduced approach, the behavior of thermoelastic waves within a homogeneous isotropic sphere in which its surface is exposed to thermal shock with varying heat source is investigated. The variations in different physical fields of a given substance have been computed by means of Laplace transform technique and an efficient numerical technique is implemented in Laplace inversion procedure. The effect of different forms of heat source are also examined and several comparisons for various thermoelasticity approaches are comprehensively conducted. [ABSTRACT FROM AUTHOR]