Search Results (335)

The motivation for this paper is that most of the works on secondary frequency control are focused on conventional synchronous communication approaches. To extend this research, this paper investigates the sampled-data-based $H_{\infty }$ load frequency control (LFC) problem for fractional-order islanded microgrids under a multi-region communication scheme. In contrast to conventional synchronous communication approaches, the proposed scheme allows each regional sensor to operate asynchronously based on its own sampling interval. To model this multi-region communication mechanism, a unified sampling sequence is constructed by collecting all sampling instants from regional sensors. Accordingly, a closed-loop system model is established through the introduction of virtual state variables. Furthermore, a novel class of looped functionals is developed to fully exploit the sampling interval characteristics of each regional sensor. By employing inequality techniques and stability analysis, sufficient conditions are derived to achieve multi-region sampled-data-based $H_{\infty }$ LFC for fractional-order islanded microgrids. In addition, a co-design method is proposed to simultaneously determine the control gain and the maximum allowable sampling period. The simulations are conducted in MATLAB/Simulink (R2024a) and the LMI conditions are solved by using the LMI Toolbox and YALMIP. Finally, comprehensive simulations in MATLAB/Simulink validate the proposed scheme. For the two-region system, the method achieves a maximum sampling period of ${\zeta }_{\max }=0.106$ s with an $H_{\infty }$ performance ratio of $2.87$ (below $\gamma =5$) and settling times of $8.5$ s and $9.2$ s. Compared to synchronous sampling, it reduces the communication bandwidth by 50% for slower regions while maintaining comparable performance. For the single-region multi-rate case ($0.104$ s and $0.140$ s sampling periods), the $H_{\infty }$ ratio is $3.12$, also satisfying $\gamma =5$. The relationship between $\gamma$ and ${\zeta }_{\max }$ is quantified: ${\zeta }_{\max }$ increases from $0.050$ s to $0.106$ s as $\gamma$ increases from 3 to 5, confirming that relaxed disturbance attenuation allows larger sampling intervals. Full article

Bamboo materials usually exhibit creep behavior under external loading conditions. This study conducted the compressive creep property research on bamboo scrimber, a commonly seen natural fiber-reinforced composite material. Firstly, the compressive creep strain data under various stress amplitudes were recorded on the basis of a four-step compressive load. Secondly, different Zener models were adopted in analyzing the recorded compressive creep process. Finally, a creep strain prediction method was proposed with the help of the verified model and the stress level-related empirical equations. The following main conclusions were drawn: for bamboo scrimber, the modified Zener model based on various-order Caputo fractional derivatives can provide precise expression in analyzing the creep performance of the material under compressive load than the traditional Zener model, as well as predict the creep strain increase property under other stress levels with a relatively shorter experimental period. Therefore, this method is valuable for promotion in modern industry. Full article

The present work is devoted to the analysis of a time-fractional Gardner equation arising in the modeling of nonlinear plasma waves in media endowed with memory and anomalous transport effects. Building on a physically motivated soliton profile, we construct a finite-time fractional ansatz in which the integer-order time variable is replaced by a fractional reparametrization that encodes the Caputo memory kernel. Within this framework, the governing evolution equation is not treated via a formal infinite expansion but rather via a finite approximation, whose quality is assessed directly via the associated residual. The Caputo fractional derivative is evaluated by a strong finite-difference formula that is second-order accurate in time and preserves the nonlocal convolution structure of the fractional operator. This combination of a finite fractional ansatz and a strong Caputo discretization allows us to compute the residual of the time analytically fractional Gardner equation and to use it as a quantitative diagnostic of accuracy and consistency. Two representative classes of nonlinear structures supported by the Gardner equation are examined in detail: a smooth solitary-wave profile and a cnoidal-wave configuration. For each example, the approximate fractional solution is generated, the corresponding residual is evaluated in space–time, and global and final-time residual norms are determined to quantify the influence of the fractional order on the wave dynamics and on the quality of the approximation. The numerical results show that the proposed residual-controlled approach yields residual magnitudes that remain one to two orders of magnitude smaller than those associated with truncated residual power-series approximations constructed from the same data, while preserving the expected qualitative features of fractional solitary and cnoidal waves in non-Markovian plasma environments. Full article

Desertification is one of the main threats to high Andean ecosystems, particularly in arid and semi-arid regions subject to increasing climatic and anthropogenic pressures. This study evaluated the spatial-temporal dynamics of desertification in the province of Candarave (Tacna, Peru) by integrating the Remote Sensing-based Desertification Index (RSDI), constructed from a principal component analysis incorporating four biophysical indicators: vegetation greenness, surface moisture, soil grain size, and fraction of solar radiation reflected (albedo), derived from Landsat 5 and 8 satellite images processed in Google Earth Engine. Temporal trends were analyzed using the Mann–Kendall test, while system stability was evaluated using the coefficient of variation, allowing different degrees of stability and environmental degradation to be characterized during the period 2010–2025. The results show that moderate and severe desertification classes predominate in higher altitude areas, covering approximately 92% of the study area, and are characterized by insignificant to weakly significant negative trends associated with high to relatively high temporal volatility. In contrast, stable areas with no significant changes represent 5.3% of the territory, while restoration processes occupy a small proportion, close to 2.7%. The high variability observed in the high Andean sectors is mainly linked to the interaction between reduced water availability, climate variability, and extreme events, as well as anthropogenic pressures, particularly overgrazing and aquifer exploitation. This multitemporal analysis allows us to anticipate the evolution of desertification and highlights the need to strengthen conservation planning in order to reduce the degradation of strategic high Andean ecosystems in the Tacna region. Full article

This paper investigates the spatial asymptotic behavior of solutions to a class of nonlinear parabolic equations defined on an exterior region in ${\mathbb{R}}^3$. By constructing a suitable weighted energy functional and employing a fractional-order differential inequality technique, we establish a sharp Phragmén–Lindelöf type alternative: the solution either ceases to exist at a finite radial distance or decays to zero as the radial variable $r\to \infty$ when the power $p>2$. In the decay case, we derive explicit polynomial type decay estimates. The analysis is conducted in unbounded exterior domains where traditional compactness arguments are not applicable, extending previous studies on semi-infinite cylinders to more complex geometric settings. Our results reveal distinct spatial behaviors compared to those observed in linear or differently nonlinear parabolic problems and can be seen as a version of Saint-Venant principle in exterior regions. Full article

Creep is one of the most important factors that should be considered during the application of composite materials in modern industry. In this work, bamboo scrimber, a commonly used natural fibre-reinforced composite material manufactured via hot pressing, was investigated to determine its creep property under compressive loading. Its creep evolution history alongside time-varying load history were analysed. In addition, variations of the Kelvin-Voigt model were used to analyse the mechanical constitutive relation of the material. The key finding of this paper is that the creep strain growth behaviour of bamboo crimper mostly depends on the stress level acting on it. Moreover, the VOF (variable-order Caputo fractional) derivative-based Kelvin-Voigt model is more suitable than the traditional model, as it simulates the dynamics of the time–strain relationship of bamboo scrimber at all relevant stress levels. The effect of stress level on the main model parameters was also analysed through detailed function models. These benefits suggest that the proposed model is significantly useful in terms of informing the design and implementation of bamboo scrimber in the real world. Full article

We report, for the first time, waimirite-(Y) in Egypt. This is only the third reported occurrence of this mineral in the world. This observation arose during our study of the rare earth element (REE) mineralization associated with the Neoproterozoic rare-metal granite intrusion in Wadi Abu Rusheid in the Eastern Desert of Egypt. The principal lanthanide and yttrium (Y) hosts in the area are waimirite-(Y) and bastnäsite-(Ce) in leucogranite and bastnäsite-(Y) in adjacent metasedimentary country rock. The leucogranite is a strongly fractionated, metaluminous to weakly peraluminous (A/CNK = 0.98–1.03), medium- to high-K calk-alkaline I-type granite. The metasediments are composed of upper greenschist to lower amphibolite-grade biotite schists with variable amounts of amphibole, graphite, and garnet. Leucogranite contains accessory Li-bearing mica, garnet, zircon, fluorite, and columbite in addition to the REE minerals. It is enriched by three orders of magnitude relative to primitive mantle in Li, Rb, Th, Ta, Nb, Pb, U, and Sn; relative to these highly enriched elements the concentrations of Sr, Ba, Ga, Zr, Hf, and Y are notably low. The REE patterns of most samples show strong enrichment in heavy relative to light REE but occasional samples have light REE-enriched patterns controlled by accessory REE minerals, and all display strong negative Eu anomalies (Eu/Eu* ≤ 0.05). The whole-rock chemistry of the metasedimentary units are different; relative to average upper continental crust they show enrichments of one to two orders of magnitude in Li, Rb, Pb, Sn, Cs, and sometimes Cr and Zn. The REE patterns of the metasedimentary units are nearly flat, with some samples showing negative Eu anomalies. Waimirite-(Y), nominally YF₃, also contains several weight percent each of Yb, Dy, and Er. The empirical formula (based on one cation) is (Y_0.55Ce_0.02Pr_0.01Nd_0.02Sm_0.02Gd_0.02Dy_0.05Er_0.04Yb_0.05Th_0.05Ca_0.16Pb_0.01)_∑1.00(F_2.48O_0.52)_∑3.00. Bastnäsite-(Ce) in leucogranite samples, nominally Ce(CO₃)F, also has several weight percent each of Nd₂O₃ and La₂O₃. The REE host in metasedimentary rocks is bastnäsite-(Y), nominally Y(CO₃)F, but also rich in Nd₂O₃ (11–19 wt.%) and La₂O₃ (4–14 wt.%). It is intimately associated with fluorophlogopite. The geochemical, mineralogical, and textural evidence indicates that waimirite-(Y) and bastnäsite-(Ce) in leucogranite crystallized from granite-derived F- and CO₂-bearing hydrothermal fluids, whereas the source of Y for growth of the bastnäsite-(Y) in the metasedimentary rocks is unclear; the large negative Ce anomaly in bastnäsite-(Y) suggests an oxidizing supergene setting. Despite their proximity, if there is a genetic connection between the mineralization in the granite and in its country rocks, the relationship is not evident from elemental patterns or host mineralogy. Full article

This article deals with the global existence and uniqueness of solutions to a fractional-order SIQR epidemic model, alongside its intricate chaotic and complex dynamics as functions of the fractional order. The well-posedness of the model solutions, including global existence, uniqueness, and positivity, is established by constructing appropriate Lyapunov functions. The local and global stability analyses are conducted for both the disease-free and endemic equilibria of the model. An asymptotic solution of the system in the form of series is derived by the Laplace–Adomian decomposition method (L–ADM), and its convergence is rigorously proved. Subsequently, numerical analysis determines and interprets the optimal truncation order of this asymptotic solution. Numerical simulations are performed based on the asymptotic solution, and the dynamics and chaos of the dynamic system with respect to the fractional order are analyzed and illustrated in terms of the maximum Lyapunov exponent and structural complexity. Finally, a local sensitivity analysis is conducted for each state variable with respect to the model parameters. Full article

Robust controller tuning is essential for the accurate regulation of nonlinear dynamic plants operating under variable conditions. This study proposes an enhanced gradient-based optimizer, termed the quadratic wavelet–enhanced gradient-based optimizer (QWS–GBO), which integrates quadratic interpolation mutation (QIM) and a wavelet mutation strategy (WMS). QIM reinforces population diversity, while WMS mitigates stagnation and strengthens local refinement through adaptive perturbations, yielding a more effective balance between global exploration and local exploitation. QWS–GBO is employed in a reference–follower control framework based on Bode’s ideal response, where the follower is realized by a fractional-order proportional–integral–derivative (FOPID) controller. The FOPID parameters are optimized using QWS–GBO and evaluated in two stages. First, performance is assessed on the CEC2020 benchmark suite under a uniform protocol. Second, the approach is applied to DC motor speed regulation. On the CEC2020 functions, QWS–GBO consistently achieves lower mean objective values and faster convergence than GBO, dwarf mongoose optimization (DMO), the arithmetic optimization algorithm (AOA), and the salp swarm algorithm (SSA) with only minor computational overhead (35.90 s per trial versus 34.00 s for GBO). In the DC motor case, the QWS–GBO–tuned FOPID controller attains a rise time of 0.0216 s, settling time of 0.0350 s, zero overshoot, and peak time of 0.0509 s. Robustness tests under four operating conditions showed limited deviations (maximum 0.0058 s in rise time, 0.0113 s in settling time, 0.465% in overshoot, and 0.0131 s in peak time). Additional analyses confirmed that both QIM and WMS individually contribute measurable gains, validating their joint integration. Implementation details and parameter settings are provided to ensure reproducibility. Full article

This study explores the interconnection between the variables of ChatGPT usage, energy consumption, water consumption, and carbon dioxide CO₂ emissions. A new integer and fractional order model using the Caputo derivative is proposed to comprehend the long-term dependencies of these variables. Boundedness, and global and local stability are examined for the fractional order model. The equilibrium points of these variables are shown to determine the stability of the model. The Runge–Kutta 7 numerical method is employed for the integer order model, whereas the semi-implicit linear interpolation (L1) method is used for the fractional order model. The parameter sensitivity is conducted on the system’s parameters to understand the variables’ impact by varying the relevant parameters for the system. To increase the efficacy of our analysis, we used machine learning approaches to model and predict the dynamics of CO₂ emissions, energy and water consumption, and ChatGPT usage. The Prophet ML model stood out among the other methods because it is adept at identifying long-term growth trends, seasonal changes, and the impact of outside variables in intricate time-series data. It is extremely beneficial for research centered on sustainability, where accurate projections are essential for wellinformed decision-making, because it can produce robust, interpretable forecasts against missing values and outliers. Using the Prophet ML model, our research guarantees precise and expandable predictions and provides valuable information that can direct tactics to balance environmental sustainability and technological progress. Full article

Time-fractional interface problems, found in heat transfer with discontinuous conductivities and fluid flows with surface tension forces, are challenging due to irregular interfaces and the history-dependent nature of fractional derivatives. This paper presents two numerical methods for simulating time-fractional double interface problems. The first method uses the Haar wavelet collocation technique, while the second relies on a meshless approach with radial basis functions. The fractional derivatives are replaced with the Caputo sense, the resulting first-order time derivatives are handled using the finite difference method, and the spatial operator is approximated using the two proposed methods. Gauss elimination is used to solve linear problems. Quasi-Newton linearization method is used for nonlinear problems. Both methods accommodate constant and variable coefficients, handling discontinuities and singularities in both solutions and coefficients. To evaluate the effectiveness of the proposed methods, numerical experiments are carried out. The accuracy of each method is quantified using the $L_{\infty }$ error norm, and a comparative analysis highlights the validity and advantages of the approaches. Moreover, the proposed schemes are rigorously analyzed to establish their stability, and the existence and uniqueness of the solutions. Full article

The origin of Mesozoic granites associated with the Dahutang W-Cu-Mo orefield in northern Jiangxi, which hosts the world’s second-largest tungsten deposit, remains a compelling subject despite extensive geochemical and geochronological studies. In this contribution, we present wolframite mineral and whole-rock geochemistry, as well as monazite and zircon U-Pb ages, for the Mesozoic granites to constrain our understanding of the petrogenesis of these granites and their coupling relationship with the mineralization. The following two magmatic phases and four types of rocks in the study area are identified: the early stage (152–147 Ma) biotite (G1) granites and the late stage (144–130 Ma) two-mica (G2),muscovite (G3), and albite (G4) granite series. These two magmatic phases are temporally coincident with two mineralization stages (~150 Ma and 144–139 Ma). All the Mesozoic granites share the characteristics of high silica content, peraluminosity (A/CNK > 1.1), and low Zr + Nb + Ce + Y values (<200 ppm); they are derived from the partial melting of a Proterozoic crustal source and classified as S-type granites. Specifically, the G1 granites are characterized by relatively high MgO (~0.5%), CaO (~1%), and low P₂O₅ (0.13%–0.20%). They formed through a relatively high degree of partial melting at approximately 766 °C (zircon saturation temperatures), a process influenced by biotite dehydration reactions, with minor contributions from mantle-derived materials. In contrast, the G2–G4 granite series exhibits more typical peraluminous S-type granite features, such as high Al₂O₃, Na₂O, and P₂O₅ (mostly > 0.2%) contents, and low Sr and Ba contents. They are products of low-degree partial melting that occurred under conditions close to muscovite breakdown at ~726 °C. Additionally, fluid–melt interaction is recorded in both granites by distinctive geochemical signatures, including enrichment in Sn (>30 ppm), Cs (>35 ppm), Li (>250 ppm), F (>0.4%), and W (10–1000 ppm), coupled with low K/Rb (<150) and Nb/Ta (<5) ratios. The near-chondritic Zr/Hf (22.6–34.1) and Y/Ho (24.5–31.5) ratios of the G1 granites imply a relatively limited role of magmatic fluid–melt interaction during its evolution. For the G2–G4 granites, however, intense crystal fractionation and late-stage fluid–melt interaction are well-documented by their highly variable and low ratios of Y/Ho (14.8–41.4), Nb/Ta (0.89–5.57), Zr/Hf (8.84–41.67), and K/Rb (13.96–128.29). In the long-lived, reduced, and volatile-rich aqueous environment of the G2–G4 magmas, fractional crystallization and albitization collectively enhanced the solubility and hydrothermal transport capacity of W, Sn, Li, Nb, and Ta by multiple orders of magnitude. In contrast, in the earlier, more oxidized G1 magmas (which incorporated mantle materials), the exsolution and hydrothermal transport of Cu and Mo were associated with localized greisenization, but their capacity diminished with fractional crystallization. Historically, mineral exploration in the Dahutang mining area has focused primarily on W, Cu, and Mo. Based on this research, we conclude that there is significant mineral potential for rare metals (particularly Sn, Li, and Ta), and future exploration should prioritize areas adjacent to the evolved G2–G4 peraluminous leucogranites to search for new concealed mineral occurrences. Full article

The Ujlayan–Dixit (UD) fractional calculus provides a powerful fractional extension of the Lomax distribution, offering a suitable framework for representing complex behaviors beyond classical approaches. In this paper, we adopt the UD fractional Lomax distribution and establish its statistical theory. Based on the adopted density, we derive closed-form expressions for the cumulative distribution, survival, and hazard functions, as well as the mode. Several UD fractional statistical measures of the Lomax random variable are derived, including the fractional moments, fractional information theoretic measures, including UD fractional Shannon and Tsallis entropy measures, and the probability density function of the $k^{th}$ order statistic under the UD fractional framework. Finally, a real data application concerning the time to break down an insulating fluid is used to illustrate the usefulness of the proposed distribution in modeling real data applications. The fitting performance of the suggested model is compared with several extensions of the Lomax distribution. The comparative results show that the UD fractional Lomax distribution outperforms several well-known extensions of Lomax distribution. This framework provides researchers with many robust tools for advanced reliability assessment, uncertainty quantification, and risk modeling, providing insights into phenomena not captured by the classical Lomax distribution. Moreover, when the fractional parameter $q\to 1^{-}$, the proposed approach converges to the classical Lomax results, bridging fractional and classical perspectives. Full article

In this article, we analyze a category of time-fractional variable-order reaction-diffusion equations coupled in the Caputo sense that are created with the modeling of complicated biological and chemical processes. Furthermore, it is shown that the solutions exist and are unique, and then the system is subjected to the Ulam-Hyers stability, which confirms the model’s reliability and robustness. An advanced solution method based on shifted second-kind Airfoil polynomials is proposed for the numerical solution, where the polynomials are used to derive an operational matrix for variable-order fractional derivatives that is then applied to the original system using the collocation method to convert it into an equivalent set of algebraic equations. The system created is solved in order to obtain very precise approximations of the unknown functions. The proposed method is illustrated through several numerical experiments that not only show its accuracy but also its efficiency. The results obtained prove that the method is superior to the currently existing numerical techniques for fractional reaction-diffusion systems. Full article

This paper investigates qualitative properties of fractional delay differential equations formulated in terms of the Atangana–Baleanu–Caputo (ABC) fractional derivative of order $1<\varrho <2$. Three related problem settings are examined: equations with variable delay, the constant-delay case, and a multi-delay extension involving several discrete delay terms. For each formulation, sufficient conditions ensuring existence and uniqueness of solutions are established in both the supremum norm and an exponentially weighted Maksoud norm. The analysis is carried out using Banach’s fixed point theorem in conjunction with progressive contractions and suitable Lipschitz-type conditions. In addition, Ulam–Hyers (UH) and Ulam–Hyers–Rassias (UHR) stability results are derived, providing quantitative estimates on the sensitivity of solutions with respect to perturbations. To complement the theoretical findings, numerical examples are presented, one of which illustrates the behavior of approximate solutions for various fractional orders. Full article