Quantum mechanics

Heat transfer

Materials science

Thermoelastic damping

Eigenvalues and eigenvectors

Economics

Thermodynamics

Physics

Mathematics

Laplace transform

Elasticity (physics)

Thermal

Mathematical analysis

Financial economics

Integral transform

Mechanics

Fractional calculus

Derivative (finance)

Waves in Random and Complex Media

A new nonlocal theory of generalized thermoelastic materials with voids based on Eringen’s nonlocal elasticity and Caputo fractional derivative is established. The one-dimensional form of the above theory is then applied to study transient wave propagation in an infinite thermoelastic materials with voids due to a time-dependent continuous heat sources distributed in a plane area. Laplace transform and eigenvalue approach techniques are used to obtain the closed form solution in the transform domain. Numerical inversions of the studied physical variables are carried out by Zakian algorithm in the space-time domain. Numerical results are plotted graphically in some cases and the results obtained are analyzed. Some comparisons for different cases are also noted.

Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer