Solid Mechanics and Its Applications Fractional Thermoelasticity

This new edition offers expanded coverage of fractional calculus, including Riemann–Liouville fractional integrals, Riemann–Liouville and Caputo fractional derivatives, Riesz fractional operators, and Mittag-Leffler and Wright functions. This new edition presents an expanded coverage of fractional calculus, including topics such as Riemann–Liouville fractional integrals, Riemann–Liouville and Caputo fractional derivatives, Riesz fractional operators, and Mittag-Leffler functions and Wright functions. Additionally, this revised edition provides a comprehensive examination of fractional heat conduction and its related theories of thermoelasticity. The reader will gain insights into the concepts of time and space nonlocality, as well as their impact on the generalizations of the Fourier law in thermoelasticity. New insights into radial heat conduction in a sphere were also added; this edition presents a detailed formulation of the problem of radial heat conduction in a sphere and the associated thermal stresses. It covers topics such as the fundamental solution to the Dirichlet problem, constant boundary conditions for temperature, and the fundamental solution to the physical Neumann problem. This new edition offers expanded coverage of fractional calculus, including Riemann–Liouville fractional integrals, Riemann–Liouville and Caputo fractional derivatives, Riesz fractional operators, and Mittag-Leffler and Wright functions. Additionally, it provides a comprehensive examination of fractional heat conduction and related theories of thermoelasticity. Readers will gain insights into the concepts of time and space nonlocality and their impact on the generalizations of Fourier's law in thermoelasticity. This edition presents a detailed formulation of the problem of heat conduction in different domains and the associated thermal stresses, covering topics such as the fundamental solution to the Dirichlet problem, constant boundary conditions for temperature, and the fundamental solution to the physical Neumann problem. New insights into time-harmonic heat impact on the boundary have also been added. Cracks in the framework of fractional thermoelasticity are also considered.