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This study aims to investigate the well‐posedness and stability of a thermoelastic Timoshenko system with non‐Fourier heat conduction. Specifically, we analyze the system using the dual‐phase‐lag (DPL) model, which incorporates two thermal relaxation times, τq$$ {\tau}_q $$ and τθ$$ {\tau}_{\theta } $$, to model non‐instantaneous heat propagation. Applying the semigroup approach, we demonstrate the existence and uniqueness of the solutions. Subsequently, we introduce a novel stability parameter ϰ$$ \varkappa $$ using the multiplier method. Exponential decay is proven for the case of ϰ=0$$ \varkappa =0 $$ with 2τθ>τq$$ 2{\tau}_{\theta }>{\tau}_q $$. Using Gearhart–Prüss theorem, we show the lack of exponential stability when ϰ≠0$$ \varkappa \ne 0 $$ and 2τθ=τq$$ 2{\tau}_{\theta }={\tau}_q $$. Numerically, we present a fully discrete approximation using the finite element method and the backward Euler scheme, and we provide some numerical simulations to show the discrete energy decay and the behavior of solutions. [ABSTRACT FROM AUTHOR]

This study investigates the three-dimensional (3-D) solitary wave interaction with two cylinders in tandem and side-by-side arrangements for two wave heights. The solitary wave generation and propagation are predicted using the volume of fluid method (VOF) coupled with the NavierStokes transport equations. The PHOENICS code is used to solve these transport equations. The solitary wave generation based on the source line developed by Hafsia et al. (2009) is extended in three-dimensional wave flow and is firstly validated for solitary waves propagating on a flat bottom. The comparison between numerical results and analytical solution for small wave height H / h = 0.1 and 0.2 shows good agreements. The wave crest and the pseudo-wavelength are well reproduced. Excellent agreements were found in terms of maximum run-up and wave forces by comparison with the present model and analytical studies. The present model can be tested for the extreme solitary wave to extend its application to a more realistic case study as the solitary wave diffraction with an offshore oil platform. [ABSTRACT FROM AUTHOR]

In this work, the exponential growth of solutions for a coupled nonlinear Klein–Gordon system with distributed delay, strong damping, and source terms is proved. Take into consideration some suitable assumptions. [ABSTRACT FROM AUTHOR]

This paper studies the dynamics of a new fractional-order map with no fixed points. Through phase plots, bifurcation diagrams, largest Lyapunov exponent, it is shown that the proposed fractional map exhibit chaotic and periodic behavior. New Hidden chaotic attractors are observed, and transient state is found to exist. Complexity of the new map is also analyzed by employing approximate entropy. Results, show that the fractional map without fixed point have high complexity for certain fractional order. In addition, a control scheme is introduced. The controllers stabilize the states of the fractional map and ensure their convergence to zero asymptotically. Numerical results are used to verify the findings. [ABSTRACT FROM AUTHOR]

In the context of the development of our study (S. Mohammed et al.) entitled "Theoretical calculation of positron-nuclear emulsion image resolution using Geant4 code" published on 2017, this research will evaluate the optimization of the image resolution of the Positron Emission Tomography (PET) when the so-called nuclear emulsion technology is introduced into tumor imaging. Upgraded and more reliable FLUKA Monte-Carlo simulation codes were performed in order to simulate a punctual source of 1 MeV positrons, emitting particles in all directions through a nuclear emulsion medium. Two new methods dedicated for the vertex reconstruction leading to an accurate recognition of the positron source are presented in this work. Moreover, this research focuses on the effects of the technical obstructions that would affect the PET imaging procedures using the nuclear emulsion, such as the scanning microscope efficiency and the actual accuracy of the slope and position measurement of the particle track on the emulsion. Taking such parameters into considerations gave a more precise and realistic estimate of the so-optimized image resolution for the PET medical imaging system. [ABSTRACT FROM AUTHOR]

This paper deals with a hyperbolic-type equation with a logarithmic source term and dynamic boundary condition. Given convenient initial data, we obtained the local existence of a weak solution. Local existence results of solutions are obtained using the Faedo-Galerkin method and the Schauder fixed-point theorem. Additionally, under suitable assumptions on initial data, the lower bound time of the blow-up result is investigated. [ABSTRACT FROM AUTHOR]

In this work, by the use of a semigroup theory approach, we provide a global solution for an initial boundary value problem of the wave equation with logarithmic nonlinear source terms and fractional boundary dissipation. In addition to this, we establish a blow-up result for the solution under the condition of non-positive initial energy. [ABSTRACT FROM AUTHOR]

In this article, we discuss the existence and uniqueness of proportional Itô–Doob stochastic fractional order systems (PIDSFOS) by using the Picard iteration method. The paper provides new results using the proportional fractional integral and stochastic calculus techniques. We have shown the convergence of the solution of the averaged PIDSFOS to that of the standard PIDSFOS in the context of the mean square and also in probability. One example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of fractional differential equations (FDEs) by using the fixed-point theory (FPT). We discuss also the Ulam–Hyers–Rassias (UHR) stability of some generalized FDEs according to some classical mathematical techniques and the FPT. Finally, two illustrative examples are presented to show the validity of our results. [ABSTRACT FROM AUTHOR]

In this work, we present the dynamics of the one dimension fractional-order Rulkov map of biological neurons. The one-dimensional neuron map shows all the dynamical behaviors observed in the real-time experiment. The integer order one-dimensional Rulkov map exhibits chaotic dynamics in the presence of time-dependent external stimuli like periodic sinusoidal force or random Gaussian process. When we construct a large complex network of neurons, the higher system dimension, as well as the external forcing, is always an obstacle. Interestingly, our study shows even with constant external stimuli, the fractional-order one-dimensional neuron shows a rich variety of complex dynamics including chaotic dynamics. We present our results based on the Lyapunov exponent of the fractional-order systems. [ABSTRACT FROM AUTHOR]

In this paper, some important objectives have been achieved, which are as follows: First, we present a method of the inverse for a class of non-singular block matrices and some associated properties. Also, the accuracy of a new method is verified with some illustrated examples by applying the MATLAB lines. Second, applying a class of block matrices, we give the exact solution for fractional matrix differential equation systems using the Laplace fractional transformation method. Finally, illustrative examples and individual cases are also presented and discussed to demonstrate our new approach. [ABSTRACT FROM AUTHOR]

The aim of this paper is two-fold. First, we investigate a finite sum involving the generalized falling factorial polynomials, in some special cases of which we express it in terms of the degenerate Stirling numbers of the second kind, the degenerate Bernoulli polynomials and the degenerate Frobenius–Euler polynomials. Second, we consider the degenerate Eulerian polynomials and deduce the generating function and a recurrence relation for them. [ABSTRACT FROM AUTHOR]

We discuss the dynamics of a fractional order discrete neuron model with electromagnetic flux coupling. The discussed neuron model is a simple one-dimensional map which is modified by considering flux coupling. We consider a discrete fractional order memristor to mimic the effects of electromagnetic flux on the neuron model. The bifurcation dynamics of the fractional order neuron map show an inverse period-doubling route to chaos as a function of control parameters, namely the fractional order of the map and the flux coupling coefficient. The bifurcation dynamics of the systems are derived both in the time and frequency domains. We present a two-parameter phase diagram using the Lyapunov exponent to categorize the various dynamics present in the system. In addition to the Lyapunov exponent, we use the entropy of the model to distinguish the various dynamics of the systems. To investigate the network behavior of the fractional order neuron map, a lattice array of N × N nodes is constructed and external periodic stimuli are applied to the network. The formation of spiral waves in the network and the impact of various parameters, like the fractional order, flux coupling coefficient and the coupling strength on the wave propagation are also considered in our analysis. [ABSTRACT FROM AUTHOR]

Recent works have focused the analysis of chaotic phenomena in fractional discrete memristor. However, most of the papers have been related to simulated results on the system dynamics rather than on their hardware implementations. This work reports the implementation of a new chaotic fractional memristor map with "hidden attractors". The fractional memristor map is developed based on a memristive map by using the Grunwald–Letnikov difference operator. The fractional memristor map has flexible fixed points depending on a system's parameters. We study system dynamics for different values of the fractional orders by using bifurcation diagrams, phase portraits, Lyapunov exponents, and the 0–1 test. We see that the fractional map generates rich dynamical behavior, including coexisting hidden dynamics and initial offset boosting. [ABSTRACT FROM AUTHOR]

In this research, we investigate the presence of weak positive solutions for a family of anisotropic non-local elliptic systems in bounded domains using the sub-super solutions approach in conjunction with Schauder's fixed point. [ABSTRACT FROM AUTHOR]

This paper presents the design of a novel methodology for robust stabilisation of distributed‐order systems, which are subject to both matched and mismatched disturbances. Matched disturbances are coped through a nonlinear controller, while mismatched disturbances are rejected by a pseudo‐state feedback, whose gain is adjusted by solving alinear matrix inequality. Since nonsmooth techniques induce not‐necessarily integer‐order differentiable solutions, the dynamical systems under consideration are defined through an operator that extends the distributed‐order differentiation of integer‐order differentiable functions to the case of not necessarily integer‐order differentiable ones. Numerical simulations highlight the reliability of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we are particularly interested in the fractional form of the Hénon-Lozi type map. Using discrete fractional calculus, we show that the general behavior of the proposed fractional order map depends on the fractional order. The dynamical properties of the new generalized map are investigated by applying numerical tools such as: phase portrait, bifurcation diagram, largest Lyapunov exponent, and 0-1 test. It shows that the fractional order Hénon-Lozi map exhibits a range of different dynamical behaviors including chaos and coexisting attractors. Furthermore, a one-dimensional control law is proposed to stabilize the states of the fractional order map. Numerical results are presented to illustrate the findings. [ABSTRACT FROM AUTHOR]

The memristor, a specialized circuit element, has found recent applications in various areas. The nonlinearity of memristors can be harnessed to construct memristive maps, capable of generating complex behavior. In this paper, we present a model of a memristive map that incorporates two memristors, two amplifiers, and a control component. The proposed model allows for adjustments not only in the number of fixed points but also in the symmetry of the memristor map. As a result, the map exhibits diverse features, including chaos, a plane of fixed points, absence of fixed points, as well as symmetry and asymmetry, which can be controlled through modifications to the control component. To facilitate quick implementation and testing of the introduced map, we employed a cost-effective microcontroller board. The experimental results demonstrate the feasibility of the map and its potential for utilization in chaos-based applications. Furthermore, the proposed model opens the door to the creation of novel memristive maps. • A simple approach to construct two-memristor based maps is proposed. • Complex dynamics of a two-memristor based map is discovered. • The map exhibits diverse features. • Hardware implementation is presented. [ABSTRACT FROM AUTHOR]

This study explores the inherent nonlinearity of quarter car models by employing an experimental and numerical approach. The dynamics of vehicular suspension systems are pivotal for ensuring passenger comfort, vehicle stability, and overall ride quality. In this paper we assessed the impact of various parameters and components on suspension performance, enabled the optimization of ride comfort, stability, and handling characteristics. Firstly, experimental analysis allowed for the investigation of factors that are challenging to model theoretically, such as stiffness nonlinearity and damping characteristics, which may vary under different operating conditions. Time domain and frequency response diagram of the model has been obtained. Secondly, a quarter-car with single degree-of-freedom presented and investigated in fractional order form. Fractional order dynamics emphasize nonlinearities in quarter car models, capturing real-world dynamics effectively. The proposed fractional-order nonlinear quarter car model employed Caputo derivative. For numerical analysis of fractional order system, the Adam-Bashforth-Moulton method is used and the disturbance of road assumed to be stochastic. Results show that the dynamic response of the vehicle can be chaotic. Influence of road roughness amplitude and frequency on vehicle vibration is investigated., (© 2024. The Author(s).)

The creation of an explicit finite difference scheme with the express purpose of resolving initial boundary value issues with linear and semi-linear variable-order temporal fractional properties is presented in this study. The rationale behind the utilization of the Caputo derivative in this scheme stems from its known importance in fractional calculus, an area of study that has attracted significant interest in the mathematical sciences and physics. Because of its special capacity to accurately represent physical memory and inheritance, the Caputo derivative is a relevant and appropriate option for representing the fractional features present in the issues this study attempts to address. Moreover, a detailed Fourier analysis of the explicit finite difference scheme's stability is shown, demonstrating its conditional stability. Finally, certain numerical example solutions are reviewed and MATLAB-based graphic presentations are made., (© 2024. The Author(s).)

The infection of human papilloma virus (HPV) poses a global public health challenge, particularly in regions with limited access to health care and preventive measures, contributing to health disparities and increased disease burden. In this research work, we present a new model to explore the transmission dynamics of HPV infection, incorporating the impact of vaccination through the Atangana-Baleanu derivative. We establish the positivity and uniqueness of the solution for the proposed model HPV infection. The threshold parameter is determined through the next-generation matrix method, symbolized by [Formula: see text]. Moreover, we investigate the local asymptotic stability of the infection-free steady-state of the system. The existence of the solutions of the recommended model is determined through fixed-point theory. A numerical scheme is presented to visualize the dynamical behavior of the system with variation of input factors. We have shown the impact of input parameters on the dynamics of the system through numerical simulations. The findings of our investigation delineated the principal parameters exerting significant influence for the control and prevention of HPV infection., (© 2024. The Author(s).)