Related papers: Fractional Dynamics of Natural Growth and Memory E…
A generalization of the economic model of logistic growth, which takes into account the effects of memory and crises, is suggested. Memory effect means that the economic factors and parameters at any given time depend not only on their…
The article discusses a generalization of model of economic growth with constant pace, which takes into account the effects of dynamic memory. Memory means that endogenous or exogenous variable at a given time depends not only on their…
Intersectoral dynamic models with power-law memory are proposed. The equations of open and closed intersectoral models, in which the memory effects are described by the Caputo derivatives of non-integer orders, are derived. We suggest…
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 standpoint of economic models in the framework of continuous time…
Standard dynamical systems approaches to economic modeling, such as those deriving the Cobb-Douglas and CES production functions from exponential growth trajectories, typically rely on integer-order differential equations. While effective,…
The most commonly developed inventory models are the classical economic order quantity model, is governed by the integer order differential equations. We want to come out from the traditional thought i.e. classical order inventory model…
We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a…
The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are…
It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…
The Solow-Swan equation is a cornerstone in the development of modern economic growth theory and continues to attract significant scholarly attention. This study incorporates memory effects into the classical Solow-Swan model by introducing…
Accelerators with power-law memory are proposed in the framework of the discrete time approach. To describe discrete accelerators we use the capital stock adjustment principle, which has been suggested by Matthews.The suggested discrete…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov…
Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the…
In this work, we investigate a fractional-order tumor growth model aimed at capturing memory effects and nonlocal temporal dynamics inherent to tumor evolution. The model is formulated using Caputo fractional derivatives and incorporates…
The Solow-Swan equation is a foundational model in the evolution of modern economic growth theory. It offers key insights into the long-term behaviour of capital accumulation and output. Since its inception, the model has served as a…
Various features of the development of individual living species, including individual humans, are programmed. Is death also programmed, and if yes, how is it implemented and what can be the underlying mechanism providing the inevitability…
Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term…
We propose a single chunk model of long-term memory that combines the basic features of the ACT-R theory and the multiple trace memory architecture. The pivot point of the developed theory is a mathematical description of the creation of…
Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by…