Related papers: On the behavior of a distributed network of capaci…
The understanding of the origin of superconductivity in cuprates has been hindered by the apparent diversity of intertwining electronic orders in these materials. We combined resonant x-ray scattering (REXS), scanning-tunneling microscopy…
We extend in this paper the definition of Caputo derivatives of order in $(0,1)$ to a certain class of locally integrable functions using a convolution group. Our strategy is to define a fractional calculus for a certain class of…
We consider fractional diffusion equation with the distributed order Caputo derivative. We prove existence of a weak and regular solution for general uniformly elliptic operator under the assumption that the weight function is only…
In this paper, we consider a class of the Caputo fractional stochastic differential equations of fractional order $\alpha \in (\frac{1}{2},1]$. Our aim is to analyze of the continuous dependence of solutions on the fractional order…
Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied, where the anomalous exponent $\beta(x) \in (0,1)$ varies in space. This type of situation occurs e.g. in biophysics, where the density of the intracellular matrix…
Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional…
Real networks are vulnerable to random failures and malicious attacks. However, when a node is harmed or damaged, it may remain partially functional, which helps to maintain the overall network structure and functionality. In this paper, we…
In this article, we propose a higher order approximation to Caputo fractional (C-F) derivative using graded mesh and standard central difference approximation for space derivatives, in order to obtain the approximate solution of time…
In this paper, an attempt is made to understand the dynamics of a fractional order three species Leslie-Gower predator prey food chain model with simplified Holling type IV functional response by considering fractional derivative in Caputo…
A numerical model based on Finite Element Method (FEM) has been developed to simulate the electrical properties of RPC utilizing the law of current conservation. It has been used to systematically investigate the effect of the electrical as…
Using closed-time path two-particle irreducible coarse-grained effective action (CTP 2PI CGEA) techniques, we study the response of an open interacting electronic system to time-dependent external electromagnetic fields. We show that the…
In this work, we present a computational analysis of the planar wave propagation behavior of a one-dimensional periodic multi-stable cellular material. Wave propagation in these materials is interesting because they combine the ability of…
A novel efficient and high accuracy numerical method for the time-fractional differential equations (TFDEs) is proposed in this work. We show the equivalence between TFDEs and the integer-order extended parametric differential equations…
This paper presents a novel First Order Plus Fractional Diffusive Delay (FOPFDD) model, capable of modeling delay dominant systems with high accuracy. The novelty of the FOPFDD is the Fractional Diffusive Delay (FDD) term, an exponential…
For describing the probability distribution of the positions and times of particles performing anomalous motion, fractional PDEs are derived from the continuous time random walk models with waiting time distribution having divergent first…
We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition…
Recent experiments in the underdoped regime of the hole-doped cuprates have found evidence for an incommensurate charge density wave state. We present an analysis of the charge ordering instabilities in a metal with antiferromagnetic…
Continuous-depth neural networks, such as the Neural Ordinary Differential Equations (ODEs), have aroused a great deal of interest from the communities of machine learning and data science in recent years, which bridge the connection…
In this paper, we present the Distributed Inter-Strand Coupling Current (DISCC) model. It is a finite element (FE) model based on a homogenization approach enabling efficient and accurate simulation of the transient magnetic response of…
Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from…