Search Results (136)

Background/Objectives: Hepatic clearance is important in determining clinical drug administration strategies. Achieving accurate hepatic clearance predictions through in vitro-to-in vivo extrapolation (IVIVE) relies on appropriate model selection, which is a critical step. Although numerous models have been developed to estimate drug dosage, some may fail to predict liver drug clearance owing to inappropriate hepatic clearance models during IVIVE. To address this limitation, an in silico-based model selection approach for optimizing hepatic clearance predictions was introduced in a previous study. The current study extends this strategy by verifying the accuracy of the selected models using ex situ experimental data, particularly for drugs whose model choices are influenced by protein binding. Methods: Commonly prescribed drugs were classified according to their hepatic extraction ratios and protein-binding properties. Building on previous studies that employed multinomial logistic regression analysis for model selection, a three-phase classification method was implemented to identify five representative drugs: diazepam, diclofenac, rosuvastatin, fluoxetine, and tolbutamide. Subsequently, an isolated perfused rat liver (IPRL) system was used to evaluate the accuracy of the in silico method. Results: As the unbound fraction increased for diazepam and diclofenac, the most suitable predictive model shifted from the initially preferred well-stirred model (WSM) to the modified well-stirred model (MWSM). For rosuvastatin, the MWSM provided a more accurate prediction. These three capacity-limited, binding-sensitive drugs conformed to the outcomes predicted by the multinomial logistic regression analysis. Fluoxetine was best described by the WSM, which is consistent with its flow-limited classification. For tolbutamide, a representative capacity-limited, binding-insensitive drug, no significant differences were observed among the various models. Conclusions: These findings demonstrate the accuracy of an in silico-based model selection approach for predicting liver metabolism and highlight its potential for guiding dosage adjustments. Furthermore, the IPRL system serves as a practical tool for validating the accuracy of the results derived from this approach. Full article

This study applies the Conformable Laplace Adomian Decomposition Method (CLADM) to solve generalized time-fractional Korteweg–de Vries (KdV) models, including seventh- and fifth-order models. CLADM combines the conformable fractional derivative and Laplace transform with the Adomian decomposition technique, offering analytic approximate solutions. Numerical and graphical results, generated using MATLAB R2020a 9.8.0.1323502, validate the method’s efficiency and precision in capturing fractional-order dynamics. Fractional parameters $\mathsf{\varrho }$ significantly influence wave behavior, with higher orders yielding smoother profiles and reduced oscillations. Comparative analysis confirms CLADM’s superiority over existing methods in minimizing errors. The versatility of CLADM highlights its potential for studying nonlinear wave phenomena in diverse applications. Full article

Grey models have attracted considerable attention as a time series forecasting tool in recent years. Nevertheless, the linear characteristics of the differential equations on which traditional grey models rely frequently result in inadequate predictive accuracy and applicability when addressing intricate nonlinear systems. This study introduces a conformable fractional order unbiased kernel-regularized nonhomogeneous grey model (CFUKRNGM) based on statistical learning theory to address these limitations. The proposed model initially uses a conformable fractional-order accumulation operator to derive distribution information from historical data. A novel regularization problem is then formulated, thereby eliminating the bias term from the kernel-regularized nonhomogeneous grey model (KRNGM). The parameter estimation of the CFUKRNGM model requires solving a linear equation with a lower order than the KRNGM model, and is automatically calibrated through the Bayesian optimization algorithm. Experimental results show that the CFUKRNGM model achieves superior prediction accuracy and greater generalization performance compared to both the KRNGM and traditional grey models. Full article

The central objective of this study is to develop some different wave solutions and perform a qualitative analysis on the nonlinear dynamics of the time-fractional chiral nonlinear Schrodinger’s equation (NLSE) in the conformable sense. Combined with the semi-inverse method (SIM) and traveling wave transformation, we establish the variational principle (VP). Based on this, the corresponding Hamiltonian is constructed. Adopting the Galilean transformation, the planar dynamical system is derived. Then, the phase portraits are plotted and the bifurcation analysis is presented to expound the existence conditions of the various wave solutions with the different shapes. Furthermore, the chaotic phenomenon is probed and sensitivity analysis is given in detail. Finally, two powerful tools, namely the variational method (VM) which stems from the VP and Ritz method, as well as the Hamiltonian-based method (HBM) that is based on the energy conservation theory, are adopted to find the abundant wave solutions, which are the bell-shape soliton (bright soliton), W-shape soliton (double-bright solitons or double bell-shaped soliton) and periodic wave solutions. The shapes of the attained new diverse wave solutions are simulated graphically, and the impact of the fractional order $\delta$ on the behaviors of the extracted wave solutions are also elaborated. To the authors’ knowledge, the findings of this research have not been reported elsewhere and can enable us to gain a profound understanding of the dynamics characteristics of the investigative equation. Full article

This study focuses on optimizing the thermal performance of hydrogen turbine blades through a sensitivity analysis using generalized fractional calculus. The approach is designed to capture the transient temperature dynamics and optimize thermal profiles by analyzing the influence of a fractional-order parameter on the system’s behavior. The model was implemented in Python, using Monte Carlo simulations to evaluate the impact of the parameter on the temperature evolution in different thermal regimes. Three distinct regions were identified: the Quasi-Uniform Region (where fractional effects are negligible), the Sub-Classical Region (characterized by delayed thermal behavior), and the Super-Classical Region (exhibiting enhanced heat accumulation). Regression analyses reveal quadratic and cubic dependencies of blade temperature on the fractional-order parameter, confirming the robustness of the model with R² values greater than 0.96. The study highlights the potential of using fractional calculus to optimize the thermal response of turbine blades, helping to identify the most suitable parameters for faster stabilization and efficient heat management in hydrogen turbines. Furthermore, it was found that by adjusting the fractional-order parameter, the system can be optimized to reach equilibrium more rapidly while achieving higher temperatures. Importantly, the equilibrium is not altered but rather accelerated based on the chosen parameter, ensuring a more efficient thermal stabilization process. Full article

This study uses a conformable derivative of order $\beta$ to investigate a fractional Whitham–Broer–Kaup ($\mathcal{FWBK}$) model. This model has significant uses in several scientific domains, such as plasma physics and nonlinear optics. The enhanced modified Sardar sub-equation $\mathcal{EMSSE}$ approach is applied to achieve precise analytical solutions, demonstrating its effectiveness in resolving complex wave photons. Bright, solitary, trigonometric, dark, and plane waves are among the various wave dynamics that may be effectively and precisely determined using the $\mathcal{FWBK}$ model. Furthermore, the study explores the chaotic behaviour of both perturbed and unperturbed systems, revealing illumination on their dynamic characteristics. By demonstrating its validity in examining wave propagation in nonlinear fractional systems, the effectiveness and reliability of the suggested method in fractional modelling are confirmed through thorough investigation. Full article

The aim of this study was to investigate the structural characteristics of four polysaccharides derived from Citri grandis fructus immaturus and their antioxidant and expectorant activities. ECP1 fraction passing through a 500 kDa dialysis bag (ECP1A) and ECP2 fraction retained in a 300 kDa dialysis bag (ECP2B) had molecular weights of 340 and 1217 kDa, respectively. All four polysaccharides were composed of six monosaccharides, including l-rhamnose, d-arabinose, d-xylose, d-mannose, d-glucose, and d-galactose, with molar ratios of 1.99:52.38:6.99:2.64:5.15:31.15 for ECP1A and 1.54:65.13:6.34:2.51:3.58:22.07 for ECP2B. ECP1A had an α/β-glucopyranose ring, and the glycosyl groups were linked mainly by 1→4, 1→2, or 1→6 glycosidic bonds. It likely adopted a single-stranded helical conformation. ECP2B had a β-glucopyranose ring, and the glycosyl groups were linked mainly by 1→4, 1→2, or 1→6 glycosidic bonds. Furthermore, in vitro experiments showed that ECP1A displayed excellent antioxidant activity (IC₅₀ = 0.4614 mg/mL). ECP2B significantly inhibited MUC5AC mucin content expression in the mucus hypersecretion model of BEAS-2B cells, thus exerting an expectorant effect. A significant negative correlation was observed between the molecular weight of Citri grandis fructus immaturus polysaccharides and their antioxidant activity, and the uronic acid and d-arabinose contents of these polysaccharides exhibited strong negative trends with both antioxidant and expectorant activities. This study shows the potential for developing and utilizing polysaccharides from Citri grandis fructus immaturus as an antioxidant and expectorant agent. Full article

This paper aims to explore sufficient conditions for the existence of mild solutions to two types of nonlocal, non-instantaneous, impulsive semilinear differential inclusions involving a conformable fractional derivative, where the linear part is the infinitesimal generator of a $C_0$-semigroup or a sectorial operator and the nonlinear part is a multi-valued function with convex or nonconvex values. We provide a definition of the mild solutions, and then, by using appropriate fixed-point theorems for multi-valued functions and the properties of both the conformable derivative and the measure of noncompactness, we achieve our findings. We did not assume that the semigroup generated by the linear part is compact, and this makes our work novel and interesting. We give examples of the application of our theoretical results. Full article

This paper investigates the oscillatory behavior of a class of mixed fractional-order nonlinear differential equations incorporating both the Liouville right-sided and conformable fractional derivatives. Symmetry plays a key role in understanding the oscillatory behavior of these systems. The motivation behind this study arises from the need for a more generalized framework to analyze oscillatory behavior in fractional differential equations, bridging the gap in the existing literature. By employing the generalized Riccati technique and the integral averaging method, we establish new oscillation criteria that extend and refine previous results. Illustrative examples are provided to validate the theoretical findings and highlight the effectiveness of the proposed methods. Full article

In this work, the viscoelastic behavior of high-density polyethylene (HDPE) and polypropylene (PP) was studied through stress relaxation experiments conducted at different strain levels. The main objective was to evaluate classical, fractional, and conformable derivatives to analyze molecular mobility, using statistical methods to identify the most accurate representation of the viscoelastic response. Besides the coefficient of determination (R²), the average absolute deviation (AAD) and mean squared error (MSE) were used as evaluation metrics, along with a multivariate analysis of variance (MANOVA) and the response surface methodology (RSM) to optimize the correspondence between experimental data and model predictions. The findings demonstrate that the spring-pot, Fractional Maxwell (FMM), Fractional Voigt–Kelvin (FVKM), and Kohlrausch–Williams-Watts (KWW) models effectively describe stress relaxation under statistical criteria. However, a joint analysis using RSM revealed that the choice of mathematical model significantly influences the outcomes. The FVKM was identified as the most effective for HDPE, while the KWW model best characterized PP. These results highlight the importance of optimization tools in advancing the characterization of polymer viscoelasticity. The ability to select the most accurate models for HDPE and PP under varying conditions can directly improve the performance and durability of products in critical industrial sectors such as packaging, automotive, and medical devices, where long-term mechanical behavior is crucial. By offering a framework adaptable to other materials and modeling approaches, this work provides valuable insights for optimizing polymer processing, improving product design, and enhancing the reliability of polymer-based components in a range of industrial applications. Full article

This study introduces a novel approach to modeling cancer tumor dynamics within a fractional framework, emphasizing the critical role of the net killing rate in determining tumor growth or decay. We explore a generalized cancer model where the net killing rate is considered across three domains: time-dependent, position-dependent, and concentration-dependent. The primary objective is to derive an analytical solution for time-fractional cancer models using the Residual Power Series Method (RPSM), a technique not previously applied in this conformable context. Traditional methods for solving fractional-order differential models face challenges such as perturbations, complex simplifications, discretization issues, and restrictive assumptions. In contrast, the RPSM overcomes these limitations by offering a robust solution that reduces both complexity and computational effort. The method provides exact analytical solutions through a convergence series and reliable numerical approximations when needed, making it a versatile tool for simulating fractional-order cancer models. Graphical representations of the approximate solutions illustrate the method’s effectiveness and applicability. The findings highlight the RPSM’s potential to advance cancer treatment strategies by providing a more precise understanding of tumor dynamics in a fractional context. This work contributes to both theoretical and practical advancements in cancer research and lays the groundwork for more accurate and efficient modeling of cancer dynamics, ultimately aiding in the development of optimal treatment strategies. Full article

In this paper, the impulsive conformable calculus approach is applied to the introduction of an $M1$ oncolytic virotherapy neural network model. The proposed model extends some existing mathematical models that describe the dynamics of the concentrations of normal cells, tumor cells, nutrients, $M1$ viruses and cytotoxic T lymphocyte (CTL) cells to the impulsive conformable setting. The conformable concept allows for flexibility in the modeling approach, as well as avoiding the complexity of using classical fractional derivatives. The impulsive generalization supports the application of a suitable impulsive control therapy. Reaction–diffusion terms are also considered. We analyze the stable behavior of sets of states, which extend the investigations of the dynamics of separate equilibrium points. By applying the impulsive conformable Lyapunov function technique, sufficient conditions for the uniform global exponential stability of sets of states are established. An example is also presented to illustrate our results. Full article

This research employs the improved modified extended tanh-function technique to explore several solitary wave solutions to the fractional-order Fokas equation. The propagation of waves in fluid dynamics and optical systems are two examples of various natural phenomena that are effectively addressed by the fractional-order Fokas equation. The model captures a generalization of the integer derivative form by including fractional derivatives defined in the conformable sense. We use the phase portrait theory to investigate the existence of traveling wave solutions. The improved modified extended tanh-function technique is successfully applied as a reliable analytical procedure to derive several solitary wave solutions, providing an approachable structure to deal with the complexity introduced by the fractional order. The extracted solutions, which are illustrated by hyperbolic, trigonometric, and rational functions, exhibit a variety of solitary wave shapes, such as bell-shaped, kink, and anti-kink patterns. We additionally evaluate how well the employed method performs in comparison to other approaches. Furthermore, some graphical visualizations are provided to clearly demonstrate the physical behavior of the obtained solutions under various parameter values. The outcomes highlight the effectiveness and adaptability of the proposed strategy in resolving fractional nonlinear differential equations and expand our knowledge of fractional-order systems. Full article

The Kuralay-II system (K-IIS) plays a pivotal role in modeling sophisticated nonlinear wave processes, particularly in the field of optics. This study introduces novel soliton solutions for the K-IIS, derived using the Riccati–Bernoulli sub-ODE method combined with Bäcklund transformation and conformable fractional derivatives. The obtained solutions are expressed in trigonometric, hyperbolic, and rational forms, highlighting the adaptability and efficacy of the proposed approach. To enhance the understanding of the results, the solutions are visualized using 2D representations for fractional-order variations and 3D plots for integer-type solutions, supported by detailed contour plots. The findings contribute to a deeper understanding of nonlinear wave–wave interactions and the underlying dynamics governed by fractional-order derivatives. This work underscores the significance of fractional calculus in analyzing complex wave phenomena and provides a robust framework for further exploration in nonlinear sciences and optical wave modeling. Full article

This study explores the application of generalized conformable derivatives in modeling hotel demand dynamics in Mexico, using the Gompertz-type model. The research focuses on customizing conformable functions to fit the unique characteristics of the Mexican hotel industry, considering the Tourist Area Life Cycle (TALC) model and aiming to enhance forecasting accuracy. The parameter adjustment in all cases was made by designing a convex function, which represents the difference between the theoretical model and real data. Results demonstrate the effectiveness of the generalized conformable derivative approach in predicting hotel demand trends, showcasing its potential for improving decision-making processes in the Mexican hospitality sector. The comparison between the logistic and Gompertz models, in both integer and fractional versions, provides insights into the suitability of these modeling techniques for capturing the dynamics of hotel demand in the studied regions. Full article