This accessible monograph is devoted to a rapidly developing area on the research of
qualitative theory of fractional ordinary differential equations and evolution equations. It is …

Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained
treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation …

Motivated by recently proposed generalizations of the diffusion-wave equation with the
Caputo time fractional derivative of order α∈(1, 2), in the present survey paper a class of …

Jeffreys equation provides an increasingly popular extension of the diffusive laws of Fourier
and Fick for heat and particle transport. Similar to generalisations of the diffusion equation …

This paper studies the existence of mild solutions and the compactness of a set of mild
solutions to a nonlocal problem of fractional evolution inclusions of order α∈(1, 2). The main …

General fractional calculus Page 119 Anatoly N. Kochubei General fractional calculus Abstract:
We describe a kind of fractional calculus and a theory of relaxation equations associated with …

Recently, numerous numerical schemes have been developed for solving single-term time-
space fractional diffusion-wave equations. Among them, some popular methods were …

We study generalized diffusion-wave equation in which the second order time derivative is
replaced by an integro-differential operator. It yields time fractional and distributed order time …

Numerous anomalous diffusion processes are characterized by crossovers of the scaling
exponent in the mean squared displacement at some correlations time. The bi-fractional …

Abstract Recent studies (see Rukolaine 2014, 2017) have deduced solutions of the
parabolic and hyperbolic dual-phase-lag (DPL) models in the three-dimensional space …