Search Results (2,212)

We investigate a numerical method for approximating stochastic Caputo fractional differential equations driven by multiplicative noise. The nonlinear functions f and g are assumed to satisfy the global Lipschitz conditions as well as the linear growth conditions. The noise is approximated by a piecewise constant function, yielding a regularized stochastic fractional differential equation. We prove that the error between the exact solution and the solution of the regularized equation converges in the $L^2((0,T)\times \mathrm{\Omega })$ norm with an order of $O(\Delta t^{\alpha -1/2})$, where $\alpha \in (1/2,1]$ is the order of the Caputo fractional derivative, and $\Delta t$ is the time step size. Numerical experiments are provided to confirm that the simulation results are consistent with the theoretical convergence order. Full article

This paper introduces a dynamic model that explores smoking and optimal control strategies. It shows how fractional-order (FO) analysis has uncovered hidden parts of complex systems and provides information about previously ignored elements. This paper uses the Bernoulli wavelet operational matrix method and the Adam–Bashforth–Moulton (ABM) method to analyse this model numerically. The mathematical model is segmented into five sub-classes: susceptible smokers, ingestion class, unusual smokers, regular smokers, and ex-smokers. It considers four optimal control measures: an anti-smoking education campaign, distribution of anti-smoking gum, administration of anti-nicotine drugs, and governmental restrictions on smoking in public areas. We show in this model how to control smoking in society strategically. Full article

Background/Objectives: Pyrostegia venusta (Cipó-de-São-João), a native Brazilian Cerrado plant, is rich antioxidant phytochemicals. The efficacy of herbal extracts, particularly their phenolic content and antioxidant potential, is influenced by the extraction method used. This study investigated the effects of two drying methods, hot-air oven drying and freeze-drying, on the antioxidant activity, cytotoxicity, and molecular interactions of aqueous extracts from the flowers and leaves of P. venusta. Methods: antioxidant capacity was assessed using DPPH, FRAP, and Folin–Ciocalteu assays; phenolic profiles were characterized by UHPLC; and cytotoxicity was evaluated via the MTT assay in HaCaT human keratinocyte cells. Additionally, in silico ADMET predictions were conducted to assess pharmacokinetics and potential toxicity, followed by molecular docking to evaluate interactions with the proliferation markers Ki-67 and PCNA. Results: that freeze-dried extracts, particularly from the flowers, contained higher concentrations of phenolic compounds and exhibited superior antioxidant activity compared to hot-air oven-dried extracts. UHPLC analysis identified a range of bioactive phenolics including caffeic, chlorogenic, gallic, ferulic, and p-coumaric acids, quercetin, and anthocyanidins such as pelargonidin-3-O-glucoside and peonidin-3-O-glucoside, with distinct compositional differences between leaves and flowers. ADMET analysis revealed generally favorable pharmacokinetic properties for most compounds. Docking simulations indicated that multiple phenolics showed synergistic interactions with Ki-67 and PCNA. Conclusions: our findings highlight freeze-drying as the optimal method for preserving bioactive compounds in P. venusta and support the therapeutic potential of its flower extracts. The evidence supports the notion that the biological effects of P. venusta are driven by synergism among multiple constituents rather than isolated compounds. Full article

Differential equations have demonstrated significant practical effectiveness across diverse fields, including physics, chemistry, biological engineering, computer science, electrical power systems, and security cryptography. This study investigates the dynamics of a Caputo fractional discrete-time modified Brusselator model. Conditions for the existence and local stability of the fixed point $FP$ are established. Using bifurcation theory, the occurrence of both period-doubling and Neimark–-Sacker bifurcations is analyzed, revealing that these bifurcations occur at specific values of the bifurcation parameter. Maximum Lyapunov characteristic exponents are computed to assess system sensitivity. Two-dimensional diagrams are presented to illustrate phase portraits, local stability regions, closed invariant curves, bifurcation types, and Lyapunov exponents, while the 0-1 test confirms the presence of chaos in the model. Finally, MATLAB simulations validate the theoretical results. Full article

This paper investigates the dispersion of atmospheric pollutants in urban environments using a fractional-order convection–diffusion-reaction model with dynamic line sources associated with vehicle traffic. The model includes Caputo fractional time derivatives and Riesz fractional space derivatives to account for memory effects and non-local transport phenomena characteristic of complex urban air flows. Vehicle trajectories are generated stochastically on the road network graph using Dijkstra’s algorithm, and each moving vehicle acts as a mobile line source of pollutant emissions. To reflect the daily variability of emissions, a time-dependent modulation function determined by unknown parameters is included in the source composition. These parameters are inferred by solving an inverse problem using synthetic concentration measurements from several fixed observation points throughout the area. The study presents two main contributions. Firstly, a detailed numerical analysis of how fractional derivatives affect pollutant dispersion under realistic time-varying mobile source conditions, and secondly, an evaluation of the performance of the proposed parameter estimation method for reconstructing time-varying emission rates. The results show that fractional-order models provide increased flexibility for representing anomalous transport and retention effects, and the proposed method allows for reliable recovery of emission dynamics from sparse measurements. Full article

This work develops a Boundary Element Method (BEM) formulation for simulating bioheat transfer in perfused biological tissues using the Atangana–Baleanu fractional derivative in the Caputo sense (ABC). The ABC operator incorporates a nonsingular Mittag–Leffler kernel to model thermal memory effects while preserving compatibility with standard boundary conditions. The formulation combines boundary discretization with cell-based domain integration to account for volumetric heat sources, and a recursive time-stepping scheme to efficiently evaluate the fractional term. The model is applied to a one-dimensional cylindrical tissue domain subjected to metabolic heating and external energy deposition. Simulations are performed for multiple fractional orders, and the results are compared with classical BEM $(a=1.0)$, Caputo-based fractional BEM, and in vitro experimental temperature data. The fractional order $a\approx 0.894$ yields the best agreement with experimental measurements, reducing the maximum temperature error to 1.2% while maintaining moderate computational cost. These results indicate that the proposed BEM–ABC framework effectively captures nonlocal and time-delayed heat conduction effects in biological tissues and provides an efficient alternative to conventional fractional models for thermal analysis in biomedical applications. Full article

Previous work has shown that mouse models fed a non-obesogenic high-fat diet have preserved cardiac function and no obesity-associated comorbidities such as diabetes. However, they do suffer increased cardiac vulnerability to ischemic reperfusion (I/R) injury, which has been attributed to changes in Ca²⁺ handling, oxidative stress, and mitochondrial transition pore activity. However, there have been no studies investigating the involvement of metabolites. Wild-type mice were fed either a control or a non-obesogenic high-fat diet for ~26 weeks. Key cardiac metabolites were extracted from freshly excised hearts and from hearts exposed to 30 min global ischemia followed by 45 min reperfusion. The extracted metabolites were measured using commercially available kits and HPLC. Hemodynamic cardiac function was monitored in Langendorff perfused hearts. Levels of energy-rich phosphates and related metabolites were similar for both hearts fed a control or a high-fat diet. However, the high-fat diet decreased cardiac glycogen and increased cardiac lactate, hypoxanthine, alanine, and taurine levels. Langendorff perfused hearts from the high-fat diet group suffered more ischemic stress during ischemia, as shown by the significantly shorter time needed for onset and for reaching maximal ischemic (rigor) contracture. Following I/R, there was a significant decrease in myocardial adenine nucleotides and a significant increase in the levels of alanine and purines for both groups. Most of the principal amino acids tended to fall during I/R. Hearts from mice fed a high-fat diet showed more changes during I/R in markers of energetics (phosphorylation potential and energy charge), metabolic stress (lactate), and osmotic stress (taurine). This study suggests that cardiac metabolic changes due to high-fat diet feeding, independent of obesity-related comorbidities, are responsible for the marked metabolic changes and the increased vulnerability to I/R. Full article

This paper proposes a novel fractional-order asset flow model based on the Atangana–Baleanu–Caputo (ABC) derivative to analyze asset price dynamics in financial markets. Compared to classical models, the proposed model incorporates a nonlocal and non-singular fractional operator, allowing for a more accurate representation of investor behavior and market adjustment processes. The model captures both short-term trend-driven responses and long-term valuation-based decisions. We establish key theoretical properties of the system, including the existence and uniqueness of solutions, positivity, boundedness, and both local and global stability using Lyapunov functions. Numerical simulations under varying fractional orders demonstrate how the ABC derivative governs the convergence speed and equilibrium behavior of the system. Compared to classical integer-order models, the ABC-based approach provides smoother dynamics, greater flexibility in modeling behavioral heterogeneity, and better alignment with observed long-term financial phenomena. Full article

Modeling risk evolution in financial networks presents both practical and theoretical challenges, particularly during periods of heightened systemic stress. This issue has gained urgency recently in China as it faces unprecedented financial strain, largely driven by structural shifts in the real estate sector and broader economic vulnerabilities. In this study, we combine Fractional-order Partial Differential Equations (FoPDEs) with network-based analysis methods, proposing a hybrid framework for capturing and modeling systemic financial risk, which is quantified using the $\Delta CoVaR$ algorithm. The FoPDEs model is formulated based on reaction–diffusion equations and discretized using the Caputo fractional derivative. Parameter estimation is conducted through a composite optimization strategy, and numerical simulations are carried out to investigate the underlying mechanisms and dynamic behavior encoded in the equations. For empirical evaluation, we utilize data from China’s financial and real estate sectors. The results demonstrate that our model achieves a Mean Relative Accuracy (MRA) of 95.5% for daily-frequency data, outperforming LSTM and XGBoost under the same conditions. For weekly-frequency data, the model attains an MRA of 91.7%, exceeding XGBoost’s performance of 90.25%. Further analysis of parameter dynamics and event studies reveals that the fractional-order parameter $\alpha$, which controls the memory effect of the model, tends to remain low when $\Delta CoVaR$ exhibits sudden surges. This suggests that the model assigns greater importance to past data during periods of financial shocks, capturing the persistence of risk dynamics more effectively. Full article

The use of solid products deriving from the pyrolysis of wastes as potential substitute of traditional binders in asphalt preparation is investigated with the final goal of reducing production costs, preserving non-renewable resources, and promoting an effective resource use as well as recovery and recycling procedures, thus implementing a regenerative circular economy approach. Char derived from the pyrolysis of agricultural and aquaculture wastes has been explored as a novel alternative additive for asphalt production. Different feedstocks were used for the preparation of biochar by pyrolysis. The produced char samples, after an in-depth chemical and structural characterization, have been implemented in the preparation of asphalt mixtures, with their potential use as a binder evaluated by performing conventional rheological tests. To evaluate the potential anti-aging effect of char as an additive, bituminous formulations containing 3 to 6 wt.% char were subjected to short-term simulated aging using the Rolling Thin-Film Oven Test (RTFOT) method. The resulting mechanical properties were then assessed. The results indicate that the all the tested char samples have limited modifying properties towards the gel-to-sol transition temperature. Among the samples, lemon peel-derived char (LP-char) showed superior antioxidant properties against bitumen oxidative aging. This study suggests that certain chemical characteristics can serve as predictive indicators of antioxidant activity in biochars produced from biomass pyrolysis. Full article

Introduction: Colorectal cancer (CRC) is the third most frequent malignancy and the second cause of cancer-related death worldwide. CRC is characterized by morphologic and biological heterogeneity, and molecular profiling is required to select appropriate treatment in the metastatic setting. Mutations in KRAS are detected in approximately 40% of CRCs, with prognostic and predictive value, and with the most frequent being p.G12D. Nonetheless, there are few data on the morphologic features in KRAS-mutated CRCs. Materials and Methods: We retrospectively collected clinicopathological features and molecular profiles of CRCs in a multicenter cohort. Results: A total of 2816 patients from 12 centers were included. KRAS mutation was found in 47.4% of cases; Gly12Asp was detected in 23.9%, with different mutation frequencies between centers. Clinicohistological features associated with Gly12Asp mutation included younger patient age (≤70 years of age), higher prevalence in males (58.6%), NOS histotype (87.1%), low pathologic grade (73.9%), high grade budding—Bd3 (43.8%), and tumoral lympho-vascular invasion (68.9%). Conclusions: Recent data have pinpointed the prognostic and predictive value of Gly12Asp mutation, and our results contribute to understanding its biology, with particular focus on peculiar clinicopathological features. Moreover, we found significant differences in pathology reports and assays for molecular profiling in different centers, which can affect a standardized therapeutic approach in CRC. Full article

This paper introduces a novel hybrid shifted Gegenbauer integral–pseudospectral (HSG-IPS) method to solve the time-fractional Benjamin–Bona–Mahony–Burgers (FBBMB) equation with high accuracy. The approach transforms the equation into a form with only a first-order derivative, which is approximated using a stable shifted Gegenbauer differentiation matrix (SGDM), while other terms are computed with precise quadrature rules. By integrating advanced techniques such as the shifted Gegenbauer pseudospectral method (SGPS), fractional derivative and integral approximations, and barycentric integration matrices, the HSG-IPS method achieves spectral accuracy. Numerical results show it reduces average absolute errors (AAEs) by up to 99.99% compared to methods like Crank–Nicolson linearized difference scheme (CNLDS) and finite integration method using Chebyshev polynomial (FIM-CBS), with computational times as low as 0.04–0.05 s. The method’s stability is improved by avoiding ill-conditioned high-order derivative approximations, and its efficiency is boosted by precomputed matrices and Kronecker product structures. Robust across various fractional orders, the HSG-IPS method offers a powerful tool for modeling wave propagation and nonlinear phenomena in fractional calculus applications. Full article

Using ultrasound-assisted extraction, we obtained a chlorophyll-rich extract from Opuntia ficus-indica cladodes (OFI) characterized through thin-layer chromatography (TLC), Fourier-transform infrared spectroscopy (FTIR), and spectrophotometric absorption analysis. The dye exhibited a strong fluorescence response in the visible range (400–800 nm) with a pronounced red emission when excited with a UV source. Antioxidant ability was evaluated via DPPH assay, showing an IC₅₀ of 185 µg/mL, highlighting its potential for reactive oxygen species scavenging. The extract was incorporated into polymethyl methacrylate (PMMA), polyvinylpyrrolidone (PVP), and polyvinyl alcohol (PVA), leading to fluorescence intensity enhancements of up to 40 times compared to the dye alone depending on matrix polarity, consistent with aggregation and polarity effects. Stability tests confirmed the dye’s resistance to CO₂ exposure, pH variations, and prolonged storage, positioning it as a viable alternative to synthetic fluorophores. These findings suggest that the OFI extract provides a functionally relevant, bio-derived dye platform promoting the valorization of agricultural by-products in high-value technological applications, highlighting a circular and scalable approach to developing ecofriendly fluorescent materials, aligning with sustainability and green technology goals. Full article

This work investigates the solutions of fractional integro-differential equations (FIDEs) using a unique kernel operator within the Caputo framework. The problem is addressed using both analytical and numerical techniques. First, the two-step Adomian decomposition method (TSADM) is applied to obtain an exact solution (if it exists). In the second part, numerical methods are used to generate approximate solutions, complementing the analytical approach based on the Adomian decomposition method (ADM), which is further extended using the Sumudu and Shehu transform techniques in cases where TSADM fails to yield an exact solution. Additionally, we establish the existence and uniqueness of the solution via fixed-point theorems. Furthermore, the Ulam–Hyers stability of the solution is analyzed. A detailed error analysis is performed to assess the precision and performance of the developed approaches. The results are demonstrated through validated examples, supported by comparative graphs and detailed error norm tables ($L_{\infty }$, $L_2$, and $L_1$). The graphical and tabular comparisons indicate that the Sumudu-Adomian decomposition method (Sumudu-ADM) and the Shehu-Adomian decomposition method (Shehu-ADM) approaches provide highly accurate approximations, with Shehu-ADM often delivering enhanced performance due to its weighted formulation. The suggested approach is simple and effective, often producing accurate estimates in a few iterations. Compared to conventional numerical and analytical techniques, the presented methods are computationally less intensive and more adaptable to a broad class of fractional-order differential equations encountered in scientific applications. The adopted methods offer high accuracy, low computational cost, and strong adaptability, with potential for extension to variable-order fractional models. They are suitable for a wide range of complex systems exhibiting evolving memory behavior. Full article

This paper investigates a novel class of weighted fuzzy fractional Volterra–Fredholm integro-differential equations (FWFVFIDEs) subject to integral boundary conditions. The analysis is conducted within the framework of Caputo-weighted fractional calculus. Employing Banach’s and Krasnoselskii’s fixed-point theorems, we establish the existence and uniqueness of solutions. Stability is analyzed in the Ulam–Hyers (UHS), generalized Ulam–Hyers (GUHS), and Ulam–Hyers–Rassias (UHRS) senses. A modified Adomian decomposition method (MADM) is introduced to derive explicit solutions without linearization, preserving the problem’s original structure. The first numerical example validates the theoretical findings on existence, uniqueness, and stability, supplemented by graphical results obtained via the MADM. Further examples illustrate fuzzy solutions by varying the uncertainty level (r), the variable (x), and both parameters simultaneously. The numerical results align with the theoretical analysis, demonstrating the efficacy and applicability of the proposed method. Full article