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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...

This book systematically presents solutions to the linear time-fractional diffusion-wave equation.It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the long-tail power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier s, Fick s and Darcy s laws are considered and different kinds of...

This book systematically presents solutions to the linear time-fractional diffusion-wave equation.It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the long-tail power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier s, Fick s and Darcy s laws are considered and different kinds of...