This new edition offers expanded coverage of fractional calculus, including RiemannLiouville fractional integrals, RiemannLiouville 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.

Provides an in-depth exploration of fractional calculus with expanded coverage of key concepts and operators Offers a comprehensive examination of fractional heat conduction and related thermoelasticity theories Enhances understanding of time and space nonlocality and their effects in thermoelasticity

Autorentext

Yuriy Povstenko received an M.S. degree in Mechanics from Lviv State University, Ukraine, in 1971; a Candidate degree (Ph.D.) in Physics and Mathematics from the Institute of Mathematics, Ukrainian Academy of Sciences, Lviv, Ukraine, in 1977; and his Doctor degree in Physics and Mathematics from Saint Petersburg Technical University, Russia, in 1993. He is currently a Professor at Institute of Mathematics and Computer Science, Jan Dlugosz University in Czestochowa, Poland. His research interests include fractional calculus, generalized thermoelasticity, nonlocal elasticity, surface science and imperfections in solids. He is the author of 5 books and more than 200 scientific papers.

Klappentext

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.

Inhalt

1. Essentials of Fractional Calculus.- 2. Fractional Heat Conduction and Related Theories of Thermoelasticity.- 3. Thermoelasticity Based on Time-Fractional Heat Conduction Equation in Polar Coordinates.- 4. Axisymmetric Problems in Cylindrical Coordinates.- 5. Thermoelasticity Based on Time-Fractional Heat Conduction Equation in Spherical Coordinates.