Fractional calculus is at this stage an arena where many models are still to be introduced,
discussed and applied to real world applications in many branches of science and …

Statistical mechanics provides a framework for describing the physics of large, complex
many-body systems using only a few macroscopic parameters to determine the state of the …

We discuss existence, uniqueness, and structural stability of solutions of nonlinear
differential equations of fractional order. The differential operators are taken in the Riemann …

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 …

Multilayer networks is a rising topic in Network Science which characterizes the structure
and the function of complex systems formed by several interacting networks. Multilayer …

Random walk is a fundamental concept with applications ranging from quantum physics to
econometrics. Remarkably, one specific model of random walks appears to be ubiquitous …

We consider an initial value problem for a class of nonlinear fractional differential equations
involving Hilfer fractional derivative. We prove existence and uniqueness of global solutions …

The optics of correlated disordered media is a conceptually rich research topic emerging at
the interface between the physics of waves in complex media and nanophotonics. Inspired …

Single particle tracking of mRNA molecules and lipid granules in living cells shows that the
time averaged mean squared displacement δ 2¯ of individual particles remains a random …

In this paper, a compact finite difference scheme for the fractional sub-diffusion equations is
derived. After a transformation of the original problem, the L1 discretization is applied for the …