Fractional Dynamics Research Articles

Impact of coastal deoxygenation on antibiotic resistance gene profiles in size-fractionated bacterial communities.

Nine years of grazing and fertilization shape dynamics of soil phosphorus fractions in Karst pasture ecosystems

This study presents a comparative analysis of breast cancer tumor growth using two mathematical approaches: the classical first-order logistic ordinary differential equation (ODE) and a fractional ODE formulation. Using fixed parameter values (intrinsic growth rate α = 0.3, intra-specific coefficient β = 0.1) and an initial tumor volume of 8 m³, numerical simulations were performed over a 0–70 day interval (step = 7 days) to obtain solution trajectories for each model. Results show that both models predict a monotonic decline in relative tumor volume over the simulated interval, but the fractional ODE consistently predicts substantially larger tumor volumes than the logistic ODE (e.g., fractional: 6.9078 → 5.2209 m³; logistic: 3.2494 → 2.9994 m³). The percentage difference between model predictions decreases over time, from about 52.96% at day 7 to about 42.55% at day 70, indicating closer agreement as the system approaches steady behavior. The paper discusses the qualitative behavior of the two model families and highlights the greater persistence of tumor volume predicted by the fractional model. Recommendations include sensitivity analyses on growth-rate and interaction coefficients to inform clinical dosing strategies and further exploration of fractional dynamics in tumor modeling.

Classical Molecular Dynamics simulations were used to investigate the interfacial adsorption of supercritical ethane on ultrathin molten polyethylene films at various temperatures (298.15–448.15 K) and pressures (0.28–13.17 MPa). Ethane was found to accumulate preferentially at the film’s interfaces rather than dissolving into the film’s core. The ultra-thin, metastable films, studied at their mechanical stability limit, are composed of two overlapping interfaces. The films show some fractions of interfacial chains transiently desorbing from the film surface and entering the gas phase, which facilitates the accumulation of ethane at the interfaces. At 373.15 K and pressures between 0.29 MPa and 9.65 MPa, the combined film interfaces adsorb between 4.8 and 8.6 times more ethane than the amount solubilized in the central, bulk region of the film. Interfacial tension of the film decreases exponentially with increasing gas pressure of ethane and is primarily governed by inter-chain interactions at the interface. Minor contributions arise from the vibrational dynamics of polyethylene chain fractions that transiently desorb from the film surface. Furthermore, the solubility of ethane in the film’s bulk region exhibits a temperature-dependent inversion: at 298.15 K, the ethane density in the film’s center slightly exceeds that of the bulk gas, but this trend reverses at 373.15 K and becomes more pronounced as the temperature increases. This indicates a potential solubility transition temperature between 298.15 K and 373.15 K.

ABSTRACTThis study investigates the dynamics of glycolytic oscillations using a time‐fractional reaction‐diffusion Goldbeter‐Lefever model with Caputo fractional derivatives. We study both the ordinary differential system (ODE) and the spatially extended system (PDE) to understand how the fractional order affects stability and pattern formation. The model extends the classical Goldbeter‐Lefever system by including memory effects through the fractional derivative. Our results show that lowering the fractional order enlarges the stability region of the steady state and changes the onset of Turing instabilities. We provide analytical conditions using linearization and spectral methods, and confirm the results with numerical simulations using a predictor‐corrector scheme and finite difference method. These results show the important role of memory and anomalous diffusion in biochemical systems. This work helps better understand how fractional dynamics affect metabolic oscillations.

ABSTRACTIn this work, we introduce a mathematical model for diabetes that uses time‐delay and variable‐order fractional derivatives, aiming to better reflect the complex and memory‐dependent behavior of glucose and insulin dynamics. The model is built using the Caputo definition of variable‐order derivatives. We explore the system's equilibrium points and examine their stability to understand how the system's behavior changes with different parameters. We also study the positivity and boundedness of the proposed system. To solve the model numerically, we design an effective method that combines a nonstandard finite difference scheme with the Grünwald–Letnikov operator. We analyze the proposed scheme and prove that the approximated solutions remain nonnegative and bounded. Through numerical simulations and comparisons, we demonstrate the reliability and practical advantages of our approach. The results highlight the crucial impact of time‐delay and variable‐order fractional dynamics on diabetes progression and treatment. Delayed insulin response and memory effects in glucose–insulin interaction are effectively modeled. This enhances the realism and personalization of blood sugar regulation analysis.

This work is a generalization of the coupled system of fractional differential equations governed by the multi-term [psi ,w]-Caputo-Fabrizio derivatives. Different fractional dynamics are supported by the kernel weight and monotone functions, and the system incorporates nonlinear, nonlocal initial conditions. Banach’s and Krasnoselskii’s fixed point theorems are applied to prove the existence, uniqueness, and Ulam-Hyers stability theorems. Furthermore, Schauder’s fixed point theorem and the controllability Gramian are used to investigate controllability conclusions for both linear and nonlinear scenarios. To demonstrate the system’s adaptability and broad applicability, several special cases are discussed. An example is provided to demonstrate how theoretical results are validated. The suggested system is used as a practical application to simulate the dynamics of an epidemic involving susceptible, infected, and recovered populations, proving the framework’s applicability and flexibility in real-world problems.

Fractional dynamics and nonlinear mixing in multi-phase porous flow: A hybrid SPH–machine learning framework

This paper investigates the asymptotic behavior of a weighted scheduled traffic process, an extension of the traditional scheduled traffic model where events are subject to random perturbations and carry variable weights. Under the assumption that the perturbations follow a heavy-tailed distribution, we demonstrate that the appropriately rescaled process converges weakly to a fractional Brownian motion. Applications of this framework span diverse fields such as queueing theory, telecommunications, finance, and healthcare, where the model provides insights into workload accumulation, network traffic variability, and transaction flow dynamics.

Mechanistic insights into organic carbon fraction sequestration in eco-engineered bauxite residue: Roles of aggregate formation and Fe/Al oxide interactions.

Abstract In this work, we investigate the use of the conformable Nikiforov–Uvarov (CNU) method to solve the radial Schrödinger equation exactly for the Coulomb potential. Analytical solutions to the radial Schrödinger equation, which describe how a quantum particle behaves under Coulomb potentials, are frequently challenging. The CNU approach allows us to convert the radial Schrödinger problem into a form that can be solved exactly by the Nikiforov–Uvarov technique, which is well known for its capacity to solve a large class of second-order linear differential equations. We apply the method to the Coulomb potential and obtain accurate formulations for the energy eigenvalues and associated wavefunctions by applying suitable boundary conditions. This method offers a strong framework for examining more intricate quantum systems and provides precise solutions for common potential models. The outcomes offer important new information on quantum mechanical systems with central potentials and demonstrate the effectiveness of the CNU approach in solving the radial Schrödinger equation, particularly when considering fractional dynamics.

This study presents a novel control approach for stabilizing the chaotic behavior of the threedimensionalfractional-order Lorenz-84 atmosphere model. By leveraging the Grünwald–Letnikov discretization method, the fractional dynamics of the system are accurately modeled. A fractional-order proportional–integral–derivative (FOPID) controller is designed, with its parameters optimally tuned using Particle Swarm Optimization (PSO). The controller adapts the input signals based on real-time state-space feedback, enabling efficient suppression of chaotic oscillations. Numerical simulations demonstrate theeffectiveness of the PSO-tuned FOPID controller in achieving precise trajectory tracking and robust stabilization. The proposed method offers a promising solution for controlling fractional-order chaotic systems in atmospheric and other nonlinear contexts.

ABSTRACTThis work addresses the numerical solution of fractional time‐dependent partial differential equations (FTPDEs) that involve the Riesz fractional derivative in space. Motivated by the effectiveness of space‐fractional operators in modeling anomalous diffusion and dispersion phenomena in mathematical physics, we extend this framework to describe classical Brownian motion using a fractional‐order formulation based on the Riesz derivative. To this end, we develop a high‐order, robust, and efficient numerical scheme for approximating the Riesz derivative, which combines both the left‐ and right‐sided Riemann–Liouville derivatives in a symmetric formulation. We perform a comprehensive analysis of the proposed method, particularly examining its stability and convergence. Furthermore, we apply this method to explore the complex dynamics of pattern formation in two important fractional reaction‐diffusion equations, which remain of significant interest in the field. Our experimental results, presented for various fractional parameter values, highlight the method's effectiveness and reveal the intricate behaviors of the system. By utilizing the Riesz fractional derivative, our approach captures the nonlocal and memory effects characteristic of fractional dynamics. This allows for more accurate modeling of phenomena where standard integer‐order methods fall short, particularly in capturing the subtleties of anomalous diffusion and pattern formation. The high‐order approximation scheme not only ensures numerical accuracy but also enhances computational efficiency, making it a valuable tool for researchers dealing with fractional partial differential equations.

We investigate a nonlinear fluid system governed by the generalized quantum-Caputo nabla fractional operator, capturing nonlocal memory effects in velocity, shear stress, and fluidity. The system is formulated with polynomial nonlinearities and modeled over the unit disk. We establish a general existence and uniqueness theorem for mild solutions in the function spaces H1(D)3, H2(D)3, and ℓ∞(D)3, based on fixed-point theory and the integral representation of the fractional operators. Under mild dissipativity assumptions, we prove boundedness and asymptotic stability using generalized (q, τ )-Mittag-Leffler decay. Furthermore, we present illustrative examples for each functional space and validate the theoretical results with numerical simulations. The findings provide a rigorous and flexible framework for modeling fractional fluid dynamics with memory-driven dissipation.

We consider first-order impulses for impulsive stochastic differential equations driven by fractional Brownian motion (fBm) with Hurst parameter H∈(12,1) involving a nonlinear ϕ-Laplacian operator. The system incorporates both state and derivative impulses at fixed time instants. First, we establish the existence of at least one mild solution under appropriate conditions in terms of nonlinearities, impulses, and diffusion coefficients. We achieve this by applying a nonlinear alternative of the Leray–Schauder fixed-point theorem in a generalized Banach space setting. The topological structure of the solution set is established, showing that the set of all solutions is compact, closed, and convex in the function space considered. Our results extend existing impulsive differential equation frameworks to include fractional stochastic perturbations (via fBm) and general ϕ-Laplacian dynamics, which have not been addressed previously in tandem. These contributions provide a new existence framework for impulsive systems with memory and hereditary properties, modeled in stochastic environments with long-range dependence.

Electronic Hong-Ou-Mandel (HOM) current noise interferometry has revealed anyonic statistics in Fractional Quantum Hall (FQH) states at ν = 1/3 and 2/5. However, hole-conjugate phases (½ < ν < 1), like ν = 2/3, host both charge and neutral edge modes, are disorder-sensitive, and pose challenges for interferometry. We present time-domain HOM and Photon-Assisted Shot Noise (PASN) measurements at ν = 2/3 to probe edge mode dynamics and tunneling charge. Using PASN’s fractional Josephson relation, we measure an e/3 tunneling charge and show that DC shot noise overestimates charge below ~100 mK. PASN reveals damping of downstream charge modes due to limited propagation of upstream neutral modes beyond a micrometer-scale equilibration length. Time-resolved HOM measurements confirm picosecond pulse broadening. These results suggest revisiting the neutral mode status, highlight the limitations of HOM interferometry in hole-conjugate phases and provide a path to explore complex FQH states that host neutral or non-Abelian modes.

Fractional dynamics of wave packets: solving the Davey-Stewartson equation with computational method

Despite its efficacy, antiretroviral therapy (ART) is not curative, and HIV-1 rebound occurs whenever treatment is interrupted. The viral reservoir in latently infected cells is the source of the infection resurgence, making it crucial to understand when and how this reservoir is established so that it can be targeted more effectively. In this study, we evaluated the decay dynamics of proviral DNA in 40 ART-naive people initiating dolutegravir-based treatment and compared these dynamics to the decay kinetics of inducible proviruses, as measured using the VIP-SPOT assay. Intensive sampling during the first month, followed by regular sampling up to 48 weeks, enabled us to outline the biphasic decay dynamics of different fractions of the viral reservoir. Our results show that the first decay phase of inducible proviruses is significantly faster than that of total HIV-1 DNA (2.6 days versus 5.1 weeks), indicating that selective pressure on this specific fraction of proviruses is particularly effective during the first days after ART initiation. These findings suggest that therapeutic interventions aimed at impacting the viral reservoir by boosting the immune response targeting the inducible fraction should be implemented at the time of, or immediately before, treatment initiation.

Targeting the intra-erythrocytic life cycle of Plasmodium falciparum unveils antimalarial drug discovery starting points from Drymaria cordata and Macaranga monandra.

Heart failure diagnosis and ejection fraction classification via feature fusion model using non-contact vital sign signals.