Resumen de Field equations and corresponding memory responses for a fiber-reinforced functionally graded medium due to heat source
Fractional derivative is a widely accepted theory to describe the physical phenomena and the processes with memory effects which is defined in the form of convolution having kernels as power functions. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. This present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena in a fiber-reinforced functionally graded unbounded medium due to the presence of periodically varying heat source in the context of three-phase-lag model of generalized thermoelasticity, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer.
Employing Laplace and Fourier transforms as tools, the problem has been solved analytically in the transformed domain. The inversion of the Fourier transform is carried out using residual calculus, and the numerical inversion of the Laplace transform has been executed using a method on Fourier series expansion. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed.
Excellent predictive capability is demonstrated due to the presence of memory dependent derivative, reinforcement, and non-homogeneity also.
