Search Results (39)

In this paper, a controlled Picard semi-analytical technique is improved for a branch of nonlinear fractional stochastic delay differential equations since the nonlinear terms always prevent the establishment of closed-form solutions. The proposed approach extends the known Picard iteration by embedding a convergence-control parameter that improves the flexibility and stability of the iterative scheme while keeping the original mathematical formulation. A careful theoretical analysis is presented to establish the existence of the iterative sequence, its mean-square boundedness, convergence, and an explicit error estimate under standard Lipschitz continuity and linear growth assumptions. Moreover, a Numerical Picard implementation is updated to rebuild stochastic sample trajectories and to give an independent illustration through comparison with a predictor–corrector scheme. The presented methodology is applied to fractional stochastic models of human postural sway and logistic population models. The numerical results illustrate that the semi-analytical framework evaluates the expectation of and variance in the stochastic response for various fractional orders accurately. Although the semi-analytical controlled Picard method is incapable of performing a lot of iterations, it generates statistical moments that agree with those obtained using both the Numerical Picard and predictor–corrector methods, while explicit semi-analytical representations of the solution. These results show that the presented technique gives an accurate and effective approach for examining nonlinear fractional stochastic delay systems from biological, ecological, and engineering applications. Full article

This paper studies mild solutions and Bolza optimal control for Riemann–Liouville fractional stochastic integro-differential systems incorporating fourth-order diffusion, time-varying control, non-instantaneous impulses, and infinite delay. Based on our self-developed $(\mu ,\nu ,\xi ,e,k)$-resolvent family, we derive the mild solution formulation and prove its existence via the Krasnoselskii–Schaefer fixed-point theorem. Using the Arzel$\acute{a}$-Ascoli theorem, Mazur’s lemma, and Balder’s lower semicontinuity principle, we further establish the existence of optimal control pairs. A numerical example from Euler–Bernoulli beam dynamics illustrates the theoretical results. Full article

This paper is concerned with the problems of mean-square global dissipativity and global asymptotic stability for a class of stochastic fractional-order memristive BAM neural networks with leakage terms and mixed time-varying delays, including discrete delays and distributed delays. By using differential inclusion theory, stochastic analysis, matrix measure approach, and Lyapunov stability theory combined with linear matrix inequalities (LMIs), several new sufficient conditions are derived to ensure the mean-square global dissipativity and global asymptotic stability of the considered system. Compared with the existing results, the obtained stability and dissipativity criteria are less conservative due to the adoption of matrix measure and fractional-order differential inequalities. The proposed model simultaneously incorporates stochastic perturbations, memristive discontinuity, leakage effects, and mixed delays, which makes it more consistent with actual engineering scenarios such as pattern recognition and intelligent control. Finally, a numerical example is provided to demonstrate the effectiveness and correctness of the theoretical results. Full article

The building façade serves as the primary interface between the built environment and external climate, marking the transition from static regulation to dynamic response in climate-adaptive design. While existing research predominantly addresses periodic climatic elements such as temperature and solar radiation, the highly stochastic wind environment and its potential for internal acoustic problems remain systematically unexplored. This study investigates the acoustic modulation mechanism of building façades under dynamic wind conditions through a simulation-based methodology. The primary aim is to demonstrate the use of active control to mitigate the influence of fluctuating wind on the internal acoustic environment of buildings with open windows or semi-open boundaries, focusing on the coupling between stochastic wind fields and architectural acoustics in humid subtropical climates. We propose a wind-responsive adaptive acoustic façade system employing fractal geometry and configurable delay strategies, and develop a high-fidelity simulation framework to quantify how façade geometry and activation logic regulate acoustic parameters under varying wind conditions (1–8 m/s). Results indicate that: (1) support vector regression-based mapping of wind speed to delay strategies maintains key sound-field parameters (Lateral Fraction (LF), Speech Clarity (C₅₀), and Early Decay Time to Reverberation Time ratio (EDT/RT₃₀)) within 10% fluctuation across wind regimes; (2) fractal configurations achieve balanced wide-band (125 Hz–8 kHz) performance, with SPL fluctuation <3 dB, spectral tilt (+0.3 dB), and reverberation time slope <0.3; (3) configurational switching between column (high LF) and row (high C₅₀) arrangements enables dynamic trade-off between spatial impression and speech clarity. This work establishes an integrated framework coupling wind dynamics, façade morphology, and acoustic modulation to regulate objective indoor acoustic parameters. Based on the simulated omnidirectional point-source model, the results show that key acoustic indicators remain stable across varying wind conditions, providing a theoretical and quantifiable basis for climate-responsive acoustic envelope design. Future work will include empirical prototype testing and listening tests to determine whether these simulated acoustic parameters translate into improved comfort and well-being for occupants. Full article

In this article, we investigate the existence and approximate controllability of a class of Sobolev-type fractional stochastic differential equations of order $1<\delta <2$ with infinite delay. The analysis is carried out in an abstract Hilbert space framework, incorporating fractional dynamics together with stochastic perturbations. By employing techniques from fractional calculus, semigroup theory, and fixed point theory, particularly the Banach contraction principle along with compactness arguments, we establish the existence of mild solutions for the proposed system. Subsequently, sufficient conditions for approximate controllability are derived by combining operator-theoretic methods with stochastic analysis. The novelty of this work lies in extending controllability results to Sobolev-type fractional stochastic systems of order $1<\delta <2$, where both the higher-order fractional structure and stochastic effects are treated simultaneously within a unified framework. This generalizes and complements several existing results in the literature that mainly address deterministic systems or fractional differential equations of order $0<\delta \le 1$. Finally, an illustrative example is presented to demonstrate the applicability and effectiveness of the theoretical findings. Full article

This study addresses the issue of nonfragile state estimation for fractional-order memristive neural networks with time-varying delays under an adaptive event-triggered mechanism. Possible gain perturbations of the estimator are considered. A Bernoulli-distributed random variable is introduced to model the stochastic nature of gain fluctuations. The primary objective is to develop a nonfragile estimator that accurately estimates the network states. By means of Lyapunov functionals and fractional-order Lyapunov methods, two delay and order-dependent sufficient criteria are established to guarantee the mean-square stability of the augmented system. Finally, the effectiveness of the proposed estimation scheme is demonstrated through two simulation examples. Full article

Fractional stochastic differential Equations (FSDEs) with time delays and non-instantaneous impulses describe dynamical systems whose evolution relies not only on their current state but also on their historical context, random fluctuations, and impulsive effects that manifest over finite intervals rather than occurring instantaneously. This combination of features offers a more precise framework for capturing critical aspects of many real-world processes. Recent findings demonstrate the existence, uniqueness, and Ulam–Hyers stability of standard fractional stochastic systems. In this study, we extend these results to include systems characterized by FSDEs that incorporate time delays and non-instantaneous impulses. We prove the existence and uniqueness of the solution for this system using Krasnoselskii’s and Banach’s fixed-point theorems. Additionally, we present findings related to Ulam–Hyers stability. To illustrate the practical application of our results, we develop a population model that incorporates memory effects, randomness, and non-instantaneous impulses. This model is solved numerically via the Euler–Maruyama method, and graphical simulations effectively depict the dynamic behavior of the system. Full article

This paper investigates the existence of square-mean S-asymptotically $(\omega ,c)$-periodic solutions for a class of neutral impulsive stochastic differential equations driven by fractional Brownian motion, addressing the challenge of modeling long-range dependencies, delayed feedback, and abrupt changes in systems like biological networks or mechanical oscillators. By employing semigroup theory to derive mild solution representations and the Banach contraction principle, we establish sufficient conditions–such as Lipschitz continuity of nonlinear terms and growth bounds on the resolvent operator—that guarantee the uniqueness and existence of such solutions in the space ${\mathcal{S}AP}_{\omega ,c}([0,\infty ),L^2(\Omega ,\mathbb{H}))$. The important results demonstrate that under these assumptions, the mild solution exhibits square-mean S-asymptotic $(\omega ,c)$-periodicity, enabling robust asymptotic analysis beyond classical periodicity. We illustrate these findings with examples, such as a neutral stochastic heat equation with impulses, revealing stability thresholds and decay rates and highlighting the framework’s utility in predicting long-term dynamics. These outcomes advance stochastic analysis by unifying neutral, impulsive, and fractional noise effects, with potential applications in control theory and engineering. Full article

This paper addresses the finite-time stability of a class of fractional Itô–Doob stochastic systems with time delays. Novel stability criteria are established using a combination of Gronwall-type, Hölder’s, and Burkholder–Davis–Gundy (BDG) inequalities, thereby generalizing classical integer-order stability theory to the fractional domain. Furthermore, the analysis uniquely integrates stochastic perturbations and time delays, providing a comprehensive framework for systems exhibiting both memory and randomness. The effectiveness of the proposed approach is demonstrated through a numerical example of a three-dimensional stochastic delayed system with fractional dynamics. Full article

In this paper, we develop a systematic review of the existing literature on the mathematical modeling of several aspects of pollinators. We selected the MathSciNet and Wos databases and performed a search for the words “pollinator” and “mathematical model”. This search yielded a total of 236 records. After a detailed screening process, we retained 107 publications deemed most relevant to the topic of mathematical modeling in pollinator systems. We conducted a bibliometric analysis and categorized the studies based on the mathematical approaches used as the central tool in the mathematical modeling and analysis. The mathematical theories used to obtain the mathematical models were ordinary differential equations, partial differential equations, graph theory, difference equations, delay differential equations, stochastic equations, numerical methods, and other types of theories, like fractional order differential equations. Meanwhile, the topics were positive bounded solutions, equilibrium and stability analysis, bifurcation analysis, optimal control, and numerical analysis. We summarized the research findings and identified some challenges that could inform the direction of future research, highlighting areas that will aid in the development of future research. Full article

This paper addresses the design of nonfragile state estimators for memristor-based fractional-order neural networks that are subject to stochastic cyber-attacks and hybrid time delays. To mitigate the issue of limited bandwidth during signal transmission, quantitative processing is introduced to reduce network burden and prevent signal blocking. In real network environments, the outputs may be compromised by cyber-attacks, which can disrupt data transmission systems. To better reflect the actual conditions of fractional-order neural networks, a Bernoulli variable is utilized to describe the statistical properties. Additionally, novel conditions are presented to ensure the stochastic asymptotic stability of the augmented error system through a new fractional-order free-matrix-based integral inequality. Finally, the effectiveness of the proposed estimation methods is demonstrated through two numerical simulations. Full article

Campylobacteriosis has been described as an ever-changing disease and health issue that is rather dangerous for different population groups all over the globe. The World Health Organization (WHO) reports that 33 million years of healthy living are lost annually, and nearly one in ten persons have foodborne illnesses, including Campylobacteriosis. This explains why there is a need to develop new policies and strategies in the management of diseases at the intergovernmental level. Within this framework, an advanced stochastic fractional delayed model for Campylobacteriosis includes new stochastic, memory, and time delay factors. This model adopts a numerical computational technique called the Grunwald–Letnikov-based Nonstandard Finite Difference (GL-NSFD) scheme, which yields an exponential fitted solution that is non-negative and uniformly bounded, which are essential characteristics when working with compartmental models in epidemic research. Two equilibrium states are identified: the first is an infectious Campylobacteriosis-free state, and the second is a Campylobacteriosis-present state. When stability analysis with the help of the basic reproduction number $R_0$ is performed, the stability of both equilibrium points depends on the $R_0$ value. This is in concordance with the actual epidemiological data and the research conducted by the WHO in recent years, with a focus on the tendency to increase the rate of infections and the necessity to intervene in time. The model goes further to analyze how a delay in response affects the band of Campylobacteriosis spread, and also agrees that a delay in response is a significant factor. The first simulations of the current state of the system suggest that certain conditions can be achieved, and the eradication of the disease is possible if specific precautions are taken. The outcomes also indicate that enhancing the levels of compliance with the WHO-endorsed SOPs by a significant margin can lower infection rates significantly, which can serve as a roadmap to respond to this public health threat. Unlike most analytical papers, this research contributes actual findings and provides useful recommendations for disease management approaches and policies. Full article

Edge computing systems must offer low latency at low cost and low power consumption for sensors and other applications, including the IoT, smart vehicles, smart homes, and 6G. Thus, substantial research has been conducted to identify optimum task allocation schemes in this context using non-linear optimization, machine learning, and market-based algorithms. Prior work has mainly focused on two methodologies: (i) formulating non-linear optimizations that lead to NP-hard problems, which are processed via heuristics, and (ii) using AI-based formulations, such as reinforcement learning, that are then tested with simulations. These prior approaches have two shortcomings: (a) there is no guarantee that optimum solutions are achieved, and (b) they do not provide an explicit formula for the fraction of tasks that are allocated to the different servers to achieve a specified optimum. This paper offers a radically different and mathematically based principled method that explicitly computes the optimum fraction of jobs that should be allocated to the different servers to (1) minimize the average latency (delay) of the jobs that are allocated to the edge servers and (2) minimize the average energy consumption of these jobs at the set of edge servers. These results are obtained with a mathematical model of a multiple-server edge system that is managed by a task distribution platform, whose equations are derived and solved using methods from stochastic processes. This approach has low computational cost and provides simple linear complexity formulas to compute the fraction of tasks that should be assigned to the different servers to achieve minimum latency and minimum energy consumption. Full article

In this paper, we present the existence of a mild solution for a class of a neutral stochastic integro-differential system over a Hilbert space. Such systems are influenced by both multiplicative and fractional noise, alongside non-instantaneous impulses, with a Hurst index H in the interval $({\displaystyle \frac{1}{2}},1)$. Additionally, the systems under consideration feature state-dependent delays (SDDs). To address this, we develop an approach to reformulate the neutral stochastic integro-differential system, incorporating SDDs and non-instantaneous impulses, into an equivalent fixed-point (FP) problem via an appropriate integral operator. By integrating stochastic analysis with the theory of resolvent operators, we employ Banach’s FP theorem to establish both the existence and uniqueness of the solution. Furthermore, we explore the Ulam–Hyers–Rassias stability of the system. Lastly, we provide illustrative examples to demonstrate the practical applicability of our results. Full article

Fractional order filters are increasingly used due to their flexibility and continuous stepped stopband attenuation rate. The current work presents a deterministic design plan for an optimal fractional-order Legendre low-pass filter along with a stochastic investigation of its parametric uncertainty. First, the filter’s order was determined using the provided parameters, then the flower pollination algorithm was used to tune the transfer function parameters. This method uses the phase delay and magnitude response functions to quantify the desired output. Circuit diagrams, LT spice simulations, and a case study were used to validate the method. In addition, the effects of various components on stability and the performance metrics were further examined. Next, each of the described fractional system parameters ($R_1$, $R_2$, the ratio ${\displaystyle \frac{R_4}{R_3}}$, $C_{\alpha }$, and $C_{\beta }$) was modeled as an uncertain term in a distinct cases, referred to as Cases I–V, respectively, and their combined effect was investigated as Case VI. These uncertain parameters were implemented using both random variables and stochastic processes. The system response was assessed using the Monte Carlo simulation method, and the mean, standard deviation, probability density function, and lower and upper bounds were plotted. Additionally, the key statistics of the cutoff frequency were tabulated in all cases. Many findings are addressed by the provided system solutions; briefly, the results revealed that the impact of uncertainty cases on system response, in descending order, was Case VI, Case III, Case V, Case II, Case I, and Case IV. Furthermore, the system demonstrated instability in Cases III and VI, which drew the designers’ attention to these two cases. Full article