Modern economics was born in the Marginal revolution and the Keynesian revolution. These
revolutions led to the emergence of fundamental concepts and methods in economic theory …

Self-similar processes are stochastic processes that are invariant in distribution under
suitable time scaling, and are a subject intensively studied in the last few decades. This …

This book contains mathematical preliminaries in which basic definitions of fractional
derivatives and spaces are presented. The central part of the book contains various …

Long-memory, or more generally fractal, processes are known to play an important role in
many scientific disciplines and applied fields such as physics, geophysics, hydrology …

Enlightened by the Caputo type of fractional derivative, here we bring forth a concept of
“memory-dependent derivative”, which is simply defined in an integral form of a common …

As is well-known, the classical Brownian motion is a stochastic process which is selfsimilar
of index 1/2 and has stationary increments. It is actually the only continuous Gaussian …

In this paper we investigate the existence, uniqueness and exponential asymptotic behavior
of mild solutions to stochastic delay evolution equations perturbed by a fractional Brownian …

Mathematical economics is a theoretical and applied science in which economic objects,
processes, and phenomena are described by using mathematically formalized language. In …

We develop a statistical theory for a continuous time approximately log‐normal fractional
stochastic volatility model to examine whether the volatility is rough, that is, whether the …

The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion
Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation …