相关论文: Fractional Logistic Growth with Memory Effects: A …
A generalization of the economic model of natural growth, which takes into account the power-law memory effect, is suggested. The memory effect means the dependence of the process not only on the current state of the process, but also on…
Bayesian multinomial logistic regression provides a principled, interpretable approach to multiclass classification, but posterior sampling becomes increasingly expensive as the model dimension grows. Prior work has studied scalability in…
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…
Fractional quantum dynamics provides a natural framework to capture nonlocal temporal behavior and memory effects in quantum systems. In this work, we analyze the physical consequences of fractional-order quantum evolution using a Green's…
We show how machine learning methods can unveil the fractional and delayed nature of discrete dynamical systems. In particular, we study the case of the fractional delayed logistic map. We show that given a trajectory, we can detect if it…
We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many…
The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the…
The partial Hamiltonian systems of the form $\dot q^i=\frac{\partial H}{\partial p_i}, \dot p^i=-\frac{\partial H}{\partial q_i}+\Gamma^i(t,q^i,p_i)$ arise widely in different fields of the applied mathematics. The partial Hamiltonian…
In this article, some logistic models in the settings of Caputo fractional operators with multi-parametered Mittag-Leffer kernels (ABC) are studied. This study mainly focuses on modified quadratic and cubic logistic models in the presence…
In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from…
Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…
Spatio-temporal forecasting plays a crucial role in various sectors such as transportation systems, logistics, and supply chain management. However, existing methods are limited by their ability to handle large, complex datasets. To…
Logistic regression is the most commonly used method for constructing predictive models for binary responses. One significant drawback to this approach, however, is that the asymptotes of the logistic response function are fixed at 0 and 1,…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
Fractional evolution equations with memory terms are widely used to model anomalous diffusion, viscoelastic response, and hereditary dynamics in physics, biology, and engineering. Among the recently introduced operators, the…
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 propose a fractional differential equation of order one-half, to model the evolution through time of the dynamics of accumulation and elimination of the contaminant in human organism with a deficient immune system, during…
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…
Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is…
We discuss explicit solutions of the logistic model with variable parameters. Classical data on the sunflower seeds growth are revisited as a simple application of the logistic model with periodic coefficients. Some applications to related…