Related papers: A Solow-Swan framework for economic growth with me…
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…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
We write down Boltzmann equation for massive particles in a spatially curved FRW universe and solve the approximate line-of-sight solution for evolution of matter density, including the effects of spatial curvature to the first order of…
Long memory in the sense of slowly decaying autocorrelations is a stylized fact in many time series from economics and finance. The fractionally integrated process is the workhorse model for the analysis of these time series. Nevertheless,…
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…
This study is a modification of the McKendrick equation into a growth model with fractional order to predict the abalone length growth. We have shown that the model is a special case of Taylor's series after it was analysed using Adomian…
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…
Epidemiological modeling is vital in understanding disease dynamics and guiding public health interventions. This study presents a time-fractional SEIR model to describe the transmission dynamics of Mpox, incorporating memory effects via…
Derivatives of fractional order with respect to time describe long-term memory effects. Using nonlinear differential equation with Caputo fractional derivative of arbitrary order $\alpha>0$, we obtain discrete maps with power-law memory.…
Understanding how spatial configurations of economic activity emerge is important when formulating spatial planning and economic policy. A simple model was proposed by Simon, who assumed that firms grow at a rate proportional to their size,…
We study a size-structured model proposed in [1] C. Barril, \`A. Calsina, O. Diekmann, J. Z. Farkas, On competition through growth reduction, e-print arXiv:2303.02981, to describe the dynamics of trees growth in the forest. Our approach to…
The Solow-Swan model is shortly reviewed from a mathematical point of view. By considering non-constant returns to scale, we obtain a general solution strategy. We then compute the exact solution for the Cobb-Douglas production function,…
Achievement and sustenance of growth are essential themes in organizational literature. In our paper, we develop models using systems thinking approach to understand how firms achieve and sustain growth in a technology-intensive product…
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed…
We introduce a multivariate multidimensional mixed-effects regression model in a finite mixture framework. We relax the usual unidimensionality assumption on the random effects multivariate distribution. Thus, we introduce a…
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…
In this paper, we investigate a fractional differential equation involving sequential Caputo derivatives, motivated by recent research on fractional models with multiple memory effects. Using techniques inspired by earlier works on…
In this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical ($\alpha=1$) differential equation in the fractional case (here using fractional…
This working paper presents a comprehensive study on the development and analysis of various electricity market models, focusing on continuous, discrete, and fractional-order approaches. The continuous model captures the ongoing…
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…