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 …

In this paper we discuss a concept of dynamic memory and an application of fractional
calculus to describe the dynamic memory. The concept of memory is considered from the …

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

Data-driven discovery of “hidden physics''---ie, machine learning of differential equation
models underlying observed data---has recently been approached by embedding the …

In this paper, a new model for financial processes in form of a space-time fractional diffusion
equation of varying order is introduced, analyzed, and applied for some financial data. While …

The purpose of this paper was to investigate the dynamics of the option pricing in the market
through the two-dimensional time fractional-order Black–Scholes equation for a European …

It is well known that the Black-Scholes model is used to establish the behavior of the option
pricing in the financial market. In this paper, we propose the modified version of Black …

In this paper, we focus on option pricing models based on time-fractional diffusion with
generalized Hilfer-Prabhakar derivative. It is demonstrated how the option is priced for …

In this article, we first provide a survey of the exponential option pricing models and show
that in the framework of the risk-neutral approach, they are governed by the space-fractional …

Since the early 1970s, the study of Black–Scholes (BS) partial differential equations (PDEs)
under the Efficient Market Hypothesis (EMH) has been a subject of active research in …