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The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…
While the coherent potential approximation (CPA) is the prevalent method for the study of disordered electronic systems, it fails to capture non-local correlations and Anderson localization. To incorporate such effects, we extend the dual…
Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient…
The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a…
We provide sharp error bounds for the difference between the transition densities of some multidimensional Continuous Time Markov Chains (CTMC) and the fundamental solutions of some fractional in time Partial (Integro) Differential…
This paper is concerned with the idea that the electron is fractionalized in the cuprate high-$T_c$ materials. We show how the notion of topological order may be used to develop a precise theoretical characterization of a fractionalized…
Infinite projected entangled-pair states (iPEPS) provide a powerful variational framework for two-dimensional quantum matter and have been widely used to capture bosonic topological order, including chiral spin liquids. Here we extend this…
The behavior of the dc-component of the current along a quantum loop of tight-binding electrons threaded by a magnetic flux that varies linearly in time Phi_M(t)= Phi t is investigated. We analize the electron transport in different kinds…
We develop a model based on the fractional exclusion statistics (FES) applicable to non-homogeneous interacting particle systems. Here the species represent elementary volumes in an (s+1)-dimensional space, formed by the direct product…
We consider an evolution equation involving the fractional powers, of order $s \in (0,1)$, of a symmetric and uniformly elliptic second order operator and Caputo fractional time derivative of order $\gamma \in (1,2]$. Since it has been…
In this paper, a delay differential equations (DDEs) model of leukemia is introduced and its dynamical properties are investigated in comparison with the modified fractional-order system where the Caputo's derivative is used. The model…
Time-fractional parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are discretised in time using collocation methods, which assume that the Caputo derivative of the computed solution is piecewise-polynomial. For…
The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…
This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional…
We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and…
Neural differential equation models have garnered significant attention in recent years for their effectiveness in machine learning applications.Among these, fractional differential equations (FDEs) have emerged as a promising tool due to…
Electronic structure of high-temperature superconducting cuprates is studied by analyzing experimental data independently obtained from two complementary spectroscopies, one, quasiparticle interference (QPI) measured by scanning-tunneling…
Distributed order fractional model of viscoelastic body is used in order to describe wave propagation in infinite media. Existence and uniqueness of fundamental solution to the generalized Cauchy problem, corresponding to fractional wave…
In this paper we present a network model to study the impact of spatial distribution of constituents, coupling between them and diffusive processes in the context of biological situations. The model is in terms of network of mobile elements…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…