Fractional Approach Research Articles

Modeling marburg virus control with limited hospital beds: a fractional approach

Abstract The Marburg virus is a serious global health threat due to its high mortality rate and rapid transmission. Effective control measures, such as hospital beds, are vital but often limited by inadequate healthcare resources. This study aims to address this challenge by developing a fractional-order epidemic model for Marburg virus, which considers the effects of limited hospital beds on transmission dynamics. We present a model to provide a more accurate understanding of Marburg virus transmission patterns and prevalence incorporating the memory effect through a fractional-order approach. The study explores the impact of constrained healthcare resources on virus progression and calculates the basic reproduction number using the next-generation matrix technique. Further analysis of the model’s global dynamics is conducted using reproduction numbers, the Lyapunov functional approach, and the Routh-Hurwitz criterion, shedding light on how hospital bed availability influences disease progression.We also apply Hyers-Ulam stability criterion to find the stability of the model and obtain numerical solutions through a fractional Lagrange two-step interpolation method. The fractional-order Marburg virus model, by accounting for memory effects, offers a more nuanced understanding of the disease dynamics compared to classical models. Our results demonstrate that increasing hospital bed availability significantly reduces Marburg virus infection rates. This approach highlights the value of fractional calculus in epidemiological modeling, offering significant insights into optimal control measures and strategies to improve public health outcomes during Marburg virus outbreaks.

The Impact of Sequential Bursting Events of Coherent Flow Structures on Sediment Entrainment at Threshold Conditions in Meandering Channel—Time Fraction Approaches

The Impact of Sequential Bursting Events of Coherent Flow Structures on Sediment Entrainment at Threshold Conditions in Meandering Channel—Time Fraction Approaches

Enhanced proteomic profiling of human plasma-derived extracellular vesicles through charge-based fractionation to advance biomarker discovery potential.

The study introduces a charge-based fractionation method for fractionating plasma-derived extracellular vesicles (EVs) into sub-populations aimed at the improved purification from free plasma proteins to enhance the diagnostic potential of EV sub-populations for specific pathophysiological states. Here, we present a novel approach for EV fractionation that leverages EVs' inherent surface charges, differentiating them from other plasma components and, thus, reducing the sample complexity and increasing the purity of EVs. The developed method was optimized and thoroughly evaluated using proteomic analysis, transmission electron microscopy, nanoparticle tracking, and western blotting of isolated EVs from healthy donors. Subsequently, we pilot-tested the developed technique for its applicability to real-world specimens using a small set of clinical prostate cancer samples and matched controls. The presented technique demonstrates the effective isolation and fractionation of EV sub-populations based on their surface charge, which may potentially help enhance EV-based diagnostics, biomarker discovery, and basic biology research. The method is designed to be straightforward, scalable, easy-to-use, and it does not require specialized skills or equipment.

Rapeseed Meal Biorefining: Fractionation, Valorization and Integration Approaches

Rapeseed meal (RSM) is an agricultural by-product with high potential as a biorefining feedstock due to its abundance, costs, and valorizable fractions, including proteins (such as cruciferin and napin), phenolics (such as sinapine and its derivatives, tannins and lignin), polysaccharides (cellulose, hemicellulose, and pectin), phytic acids and glucosinolates. RSM is also an important candidate for a whole-crop biorefining scheme, due to its integration potential with biorefining of other rapeseed-derived fractions, including rapeseed oil and straw. To date, research and development into holistic integrated RSM biorefining is limited, with the majority of the literature focusing on the valorization of a single fraction, typically proteins or phenolics, overlooking the potential of other fractions as well as the post-processing residue. This review is designed to aid efforts to develop a holistic RSM biorefining scheme through a comprehensive assessment of processing and applications of valorizable RSM fractions within an integrated biorefining context. The myriad of extraction, purification, modification, and applications for each fraction are discussed to elucidate their valorization potential and highlight major gaps within the literature that need to be addressed in the future. Finally, the current literature on RSM biorefinery and a proposal for a more holistic integrated biorefinery scheme are discussed and important considerations, challenges, and future steps for the development of RSM and rapeseed biorefinery are provided. The perspective, insights, and recommendations provided by this review will be beneficial for the future development of holistic integrated biorefineries for rapeseed and other biomass feedstocks in general.

Objective Bayesian Model Selection for Spatial Hierarchical Models with Intrinsic Conditional Autoregressive Priors

We develop Bayesian model selection via fractional Bayes factors to simultaneously assess spatial dependence and select regressors in Gaussian hierarchical models with intrinsic conditional autoregressive (ICAR) spatial random effects. Selection of covariates and spatial model structure is difficult, as spatial confounding creates a tension between fixed and spatial random effects. Researchers have commonly performed selection separately for fixed and random effects in spatial hierarchical models. Simultaneous selection methods relieve the researcher from arbitrarily fixing one of these types of effects while selecting the other. Notably, Bayesian approaches to simultaneously select covariates and spatial model structure are limited. Our use of fractional Bayes factors allows for selection of fixed effects and spatial model structure under automatic reference priors for model parameters, which obviates the need to specify hyperparameters for priors. We also show the equivalence between two ICAR specifications and derive the minimal training size for the fractional Bayes factor applied to the ICAR model under the reference prior. We perform a simulation study to assess the performance of our approach and we compare results to the Deviance Information Criterion and Widely Applicable Information Criterion. We demonstrate that our fractional Bayes factor approach assigns low posterior model probability to spatial models when data is truly independent and reliably selects the correct covariate structure with highest probability within the model space. Finally, we demonstrate our Bayesian model selection approach with applications to county-level median household income in the contiguous United States and residential crime rates in the neighborhoods of Columbus, Ohio.

Endogenous HiBiT-tagging combined with affinity complementation: A new strategy for small open reading frame-encoded polypeptide detection in bacteria

Bacterial genome annotations are continuously refined with the advent of novel techniques. Ribosome profiling, or Ribo-seq, utilizing next-generation sequencing to link genomic regions with translational activity, has uncovered numerous small open reading frames (sORFs) - arbitrarily defined as ORFs no longer than 300 base pairs - as a generally under-annotated class of genomic elements in both eukaryotic and prokaryotic genomes. While sORFs can function as regulatory elements, they may also translate into small proteins (equal to or shorter than 100 amino acids), classified as sORF-encoded polypeptides (SEPs). The inherent limitations of ribosome profiling necessitate the experimental validation of predicted (s)ORFs at the protein expression level. However, the small size and unique biochemical characteristics of SEPs pose significant challenges for traditional protein detection methods, like mass spectrometry and immunoblotting. In this study, we introduce HiBiT blotting, a luminescent, complementation-based protein detection method, as a highly sensitive alternative to antibody-based immunoblotting for investigating SEP expression in Salmonella enterica (serovar) Typhimurium (S. Typhimurium) at endogenous levels. We demonstrate its complementarity to mass spectrometry as an expression validation tool. Additionally, employing a biochemical fractionation approach, we determined the subcellular localization of validated S. Typhimurium SEPs, initiating exploration into the functional aspects of these SEPs, and proposed enrichment strategies that may facilitate future experimental validation of Ribo-seq-predicted sORFs.

Mathematical modeling of tuberculosis transmission dynamics with vaccination and two lines of treatments: a caputo fractional approach

Mathematical modeling of tuberculosis transmission dynamics with vaccination and two lines of treatments: a caputo fractional approach

Response Analysis and Vibration Suppression of Fractional Viscoelastic Shape Memory Alloy Spring Oscillator Under Harmonic Excitation

This study investigates the dynamic behavior and vibration mitigation of a fractional single-degree-of-freedom (SDOF) viscoelastic shape memory alloy spring oscillator system subjected to harmonic external forces. A fractional derivative approach is employed to characterize the viscoelastic properties of shape memory alloy materials, leading to the development of a novel fractional viscoelastic model. The model is then theoretically examined using the averaging method, with its effectiveness being confirmed through numerical simulations. Furthermore, the impact of various parameters on the system’s low- and high-amplitude vibrations is explored through a visual response analysis. These findings offer valuable insights for applying fractional sliding mode control (SMC) theory to address the system’s vibration control challenges. Despite the high-amplitude vibrations induced by the fractional order, SMC effectively suppresses these vibrations in the shape memory alloy spring system, thereby minimizing the risk of catastrophic events.

How good are the dynamical results obtained through different terminators of a continued fraction approach?

Extrapolation procedures for obtaining higher order recurrants within the Method of Recurrence Relation have been analyzed considering one-dimensional spin-1/2 quantum systems comprising the isotropic XY model, the random transverse Ising model, and the isotropic Heisenberg model. The first six recurrants have already been computed for the XY model, as well as nine recurrants for the random transverse Ising model, and fourteen recurrants for the Heisenberg model. Nevertheless, from the exact solution of the autocorrelation function and its spectral density, it has been possible here to exactly compute all orders of the moments and recurrants for the XY model. An analytical expression for the recurrants of the XY model has also been proposed, which is able to furnish all of the recurrants, of any order, to within only 0.03 percent error. An extrapolation process has then been employed to analyze the autocorrelation functions and their spectral densities for all three models. It has been noticed that, as expected, the more recurrants are estimated the longer is the timespan of the computed autocorrelation function. However, the timespan saturates and becomes insensitive as more recurrants are taken into accout. On the other hand, the autocorrelation function needs a high number of recurrants in order to obtain a quantitative account of the spectral function. Even so, the behavior of the spectral density still remains, in cases where just a few recurrants are exactly known, not completely clear in the low frequency region.

Effects of Memory on Inventory Control and Pricing Policy for Imperfect Production with Rework Process

Fractional calculus is a pertinent way to study the memory effect in an inventory model for investigating its dynamical behavior. Since inventory management is a memory-dependent process, fractional calculus approach may be employed to discover some fruitful insights and can help to gain more profit. In realistic scenarios, the manufacturing process cannot be perfect, and it delivers some faulty units due to many inevitable reasons. In literature, an imperfect production inventory problem under the memory effect has not been studied. Our study aims to investigate the memory effect on a production inventory system. In this article, a fractional order inventory control problem is formulated by considering an imperfect manufacturing process and price-sensitive demand. The faulty units are repaired through a rework process. Caputo fractional derivatives and integrals are used to consider the memory effect. Due to the nonlinear cost elements in the formulated problem, optimal pricing and production policies are investigated by using a quasi-Newton optimization algorithm and particle swarm optimization approach. The managerial implications of the proposed study are discussed with the help of numerical illustrations. The numerical outcomes suggest that consideration of memory in the inventory system boosts the profitability of the firm.

A New Fractional Approach for the Higher-Order q-Taylor Method

The main goal of this work is to propose a new fractional approach of the higher order q-Taylor method with Initial Value Problems (IVPs) for fractional q-difference equations which is called the Fractional Higher-Order q-Taylor Method (FHOqTM). By applying the generalised q-Taylor theorem, this would be achieved. As a consequence, we calculate the FHOqTM’s local truncation error. Finally, we present numerical applications to validate our results by comparing the exact solution and the approximatesolution resulting from (FHOqTM).

Predicting Natural Gas Production in Various Nations Using a Fractional Grey Bernoulli Approach

Accurate forecasting of natural gas production is crucial for economic stability, environmental sustainability, and market investment. This study presents an advanced forecasting method using the fractional grey Bernoulli model, which combines fractional accumulation and Bernoulli processes to enhance the predictive accuracy for nonlinear datasets. The model’s versatility and flexibility allow it to adapt to various data characteristics and complexities, thereby outperforming traditional grey models in forecasting performance. To optimize the model parameters, this study employs the Particle Swarm Optimization (PSO) algorithm, further improving the model’s effectiveness. Empirical analysis of natural gas production data from Brazil, Italy, and Qatar demonstrates that the model exhibits significant advantages in both fitting and forecasting capabilities. The findings indicate that the fractional grey Bernoulli model achieves high accuracy and reliability in predicting natural gas production in these countries, providing a robust framework for strategic energy planning and investment decision-making. With average forecast errors of 1.9113%, 4.0353%, and 1.8902% for natural gas production in Brazil, Italy, and Qatar respectively, this study underscores the model’s effectiveness in enhancing forecast reliability and minimizing risk, providing valuable insights for sustainable energy development.

A Novel Approach for Time-Local Fractional Solutions of Certain Nonlinear Partial Differential Equations in Fractal Dimension

Time-local fractional approaches for nonlinear partial differential equations in fractal dimensions are essential for capturing the complex, irregular behaviors found in fractal systems. In this paper, a new modification of the local fractional Laplace variational iteration method (MLFLVIM) for obtaining analytical approximate solutions to the fractional gas dynamics equation, fractional Stefan equation, and fractional Newell-Whitehead-Segel equation within the context of fractal time space is presented. The proposed method (MLFLVIM) elegantly combines the local fractional Laplace transform (LFLT) with modified variational iteration method. Specifically, we first apply the (LFLT) to the given local fractional PDEs, yielding a transformed system of equations. We then apply modified variational iteration to this system. Finally, we use the inverse of (LFLT) to obtain the desired solution. To demonstrate the effectiveness of this approach, we implement it on three numerical physical problems. The results show that the (MLFLVIM) can successfully handle these nonlinear LFPDEs and provide accurate analytical approximation solutions.

Understanding perspectives for mixed mode oscillations of the fractional neural network approaches to the analysis of neurophysiological data from the perspective of the observability of complex networks

Understanding perspectives for mixed mode oscillations of the fractional neural network approaches to the analysis of neurophysiological data from the perspective of the observability of complex networks

Bioassay-guided isolation and in Silico characterization of cytotoxic compounds from Hemimycale sp. Sponge targeting A549 lung cancer cells

Bioassay-guided fractionation approach led to identification of two novel compounds; (4-(hydroxymethyl)-3-methoxy-1H-pyrazol (1) and mycalene (2), alongside with four known metabolites; octadecane (3), hexatriacontane (4), 1-heneicosanol (5) and heptatriacontanoic acid (6) from the Red Sea marine sponge Hemimycale sp. The ethyl acetate fraction showed a noticeable cytotoxic activity against the lung cancer cell line (A549) with IC50 value of 75.54 µg/ mL. Structural elucidation was achieved using a combination of 1D and 2D nuclear magnetic resonance (NMR) spectroscopy and high-resolution electrospray ionization-mass spectrometry (HR-ESI-MS). To elucidate the potential mechanism of action behind the cytotoxic effects against lung cancer, a multi-faceted approach combining in silico network pharmacology, experimental validation, and molecular docking studies were employed. Both compounds, designated as 1 and 2, demonstrated significant binding affinities to predicted target proteins, with docking scores of -4.789 and − 4.421 kcal/mol, respectively. These results lay the groundwork for further investigation into the therapeutic potential of these novel compounds from Hemimycale sp. as promising candidates for lung cancer treatment.

A Novel Approach to Solving Fractional Diffusion Equations Using Fractional Beta Derivative

This paper introduces a novel application of fractional beta derivatives in solving fractional diffusion equations with an emphasis on systems exhibiting anomalous diffusion and memory effects. The work explores the fractional beta derivative as an extension of classical fractional derivatives by incorporating a parameter β (beta) that controls the system’s memory behavior. We investigate both the analytical and numerical solutions of these equations, demonstrating the superior flexibility of fractional beta derivatives in modeling complex diffusion processes. Additionally, we provide a comparison between classical fractional derivatives and the new fractional beta approach to highlight the advantages in terms of accuracy and computational efficiency. We begin by reviewing the theoretical background of fractional derivatives and proceed to introduce the beta derivative as a modification that provides additional flexibility in modeling complex systems. Applications in fields such as control theory, signal processing, and bioengineering are highlighted. Furthermore, numerical methods for solving fractional beta differential equations are discussed, along with potential areas for future research.

Enhancing the strength of tissue paper through pulp fractionation and stratified forming

Abstract The potential of combining stratified paper forming with pulp fractionation was investigated to improve the balance between low density, which enhances water absorbency and softness, and the dry strength of tissue papers. The selected fractionation approaches allowed us to separate especially stiff, low-fibrillated fibers (A fractions) from flexible, fibrillated fibers containing fines (detached segments of fibers, fibrils, or lamellae fragments) (B fractions). After characterizing the morphological properties of each fiber fraction, 20 g/m2 model papers were produced with and without wet pressing to tune the paper density. At a density of 0.3 g/cm³, the tensile breaking stress of B papers was at least three times higher than that of A papers. The strain at break of B papers was also close to two times higher than that of A papers. Interestingly, bilayer papers A/B exhibited breaking stress values intermediate between those of A and B papers, while native pulp papers, i.e., without fractionation and stratified forming, followed the trend of A papers. Notably, bi-layering the paper improved the breaking stress by up to twice as much without increasing the paper density, which could be highly beneficial in improving the balance of properties in tissue paper grades.

Fractional mimetic dark matter: A fractional action-like variational approach

In this paper, we propose a nonlocal extension of the mimetic dark matter model based on the FALVA implementation of fractional calculus. Our primary objective to explore how certain properties of dark matter can be modeled within the FALVA framework rather than formulate a phenomenological model. We begin by constructing the action functional of the cosmological extension of the mimetic dark model and deriving the nonlinear equations of motion in the general case. Next, we focus on a fractional-power homogeneous mimetic dark field with an exponential expansion factor. We derive the equation of motion for the lapse field and obtain its general solution. Analytical solutions are then obtained for small time intervals and arbitrary values of the fractionality parameter. These solutions enable us to establish the physical line element of spacetime, incorporating the mimetic dark matter field. From this line element, we derive the Ricci tensor, Ricci scalar, and geodesic equations.

A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations

A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations

Modeling Ebola Dynamics with a Φ-Piecewise Hybrid Fractional Derivative Approach

Ebola virus disease (EVD) is a severe and often fatal illness posing significant public health challenges. This study investigates EVD transmission dynamics using a novel fractional mathematical model with five distinct compartments: individuals with low susceptibility (S1), individuals with high susceptibility (S2), infected individuals (I), exposed individuals (E), and recovered individuals (R). To capture the complex dynamics of EVD, we employ a Φ-piecewise hybrid fractional derivative approach. We investigate the crossover effect and its impact on disease dynamics by dividing the study interval into two subintervals and utilize the Φ-Caputo derivative in the first interval and the Φ-ABC derivative in the second interval. The study determines the basic reproduction number R0, analyzes the stability of the disease-free equilibrium and investigates the sensitivity of the parameters to understand how variations affect the system’s behavior and outcomes. Numerical simulations support the model and demonstrate consistent results with the theoretical analysis, highlighting the importance of fractional calculus in modeling infectious diseases. This research provides valuable information for developing effective control strategies to combat EVD.