Search Results (69)

Background/Objectives: Intranasal tumors are common malignancies in dogs, characterized by locally aggressive behavior and clinical signs such as epistaxis, nasal discharge, and facial deformity. Radiotherapy (RT) is considered the treatment of choice due to anatomical limitations to surgical resection. This study aimed to evaluate clinical outcomes, toxicity, and prognostic factors in dogs with primary malignant intranasal tumors treated with cobalt-60–based megavoltage radiotherapy. Methods: This retrospective study included 40 dogs with histopathologically confirmed primary malignant intranasal tumors treated between September 2018 and February 2025 at a veterinary radiotherapy clinic in Rio de Janeiro, Brazil. Medical records were reviewed for patient demographics, tumor characteristics, treatment protocols, response, toxicity, and survival outcomes. Tumors were staged using modified Adams criteria based on computed tomography. Definitive-intent protocols (n = 32) delivered 48–54 Gy in 10–13 fractions administered three to five times weekly, while palliative protocols consisted of either four fractions of 8 Gy delivered once weekly or five fractions of 4 Gy delivered daily. Results: Adenocarcinoma was the most common histologic subtype (42.5%), and 82.5% of dogs had stage III–IV disease. The objective response rate was 82.5% (CR: 17.5%; PR: 65.0%), with clinical benefit observed in 92.5% of cases. Acute toxicity was frequent but manageable, primarily affecting skin, oral mucosa, and eyes. Overall median progression-free interval (PFI) and survival time (MST) were 382 days and 430 days, respectively. Stage IV disease was significantly associated with shorter survival when compared to stage I-III (MST 345 vs. 1063 days, respectively; p = 0.016). Treatment response was significantly associated with PFI in univariate analysis (p < 0.05). Conclusions: Radiotherapy provided high response rates and meaningful clinical benefit with acceptable toxicity in dogs with malignant intranasal tumors, highlighting the importance of early diagnosis and treatment. Further prospective studies with standardized protocols are warranted. Full article

This study models trachoma transmission in Cameroon using a deterministic approach with integer and fractional-order derivatives, incorporating direct, fly-mediated, and environmental transmission routes. Fitting disease data from 1990–2019, the model forecasts trachoma prevalence until 2035. The research confirms the solution existence and uniqueness, calculates the basic reproduction number ${\mathcal{R}}_0^{\lambda }$ where $\lambda \in (0,1]$ represents the fractional-order parameter, and analyzes equilibrium stability. A stable trachoma-free equilibrium exists when ${\mathcal{R}}_0^{\lambda }<1$, while an endemic equilibrium is proven stable for ${\mathcal{R}}_0^{\lambda }>1$ under specific conditions. Calibration of a fractional model with Cameroon data yielded an ${\mathcal{R}}_0$ of 1.169 (indicating endemicity) and identified an optimal fractional order of $\lambda =0.98$. By calculating the strength number, we found that another epidemic wave could occur in 50 years. Global sensitivity analysis highlighted key parameters affecting trachoma dynamics. A numerical scheme of the model based on the Adams–Bashforth–Moulton method is constructed and its stability demonstrated. It is then used to perform several numerical simulations, first to validate the theoretical results obtained, and then to compare the different models (statistical and deterministic). The conclusion is reached that the disease will persist in the population (${\mathcal{R}}_0>1$), although the statistical model shows that it could disappear by 2030. This proves that, for trachoma dynamics in Cameroon, it is advisable to use a deterministic model. Full article

This paper presents a unified analytical and computational framework for the study of typhoid fever transmission dynamics governed by a Caputo fractional-order compartmental model of order $\kappa \in (0,1]$. The population is stratified into five epidemiological classes, namely susceptible $\left(\mathcal{S}\right)$, asymptomatic $\left(\mathcal{A}\right)$, symptomatic $\left(\mathcal{I}\right)$, hospitalised $\left(\mathcal{H}\right)$, and recovered $\left(\mathcal{R}\right)$, and the governing system explicitly incorporates asymptomatic transmission, treatment dynamics, and temporary immunity with waning. The use of the Caputo fractional derivative is motivated by the well-documented existence of chronic asymptomatic Salmonella Typhi carriers, whose heavy-tailed sojourn times in the carrier state are naturally encoded by the Mittag–Leffler waiting-time distribution arising from the fractional operator. A complete qualitative analysis of the fractional system is carried out: the basic reproduction number ${\mathcal{R}}_0$ is derived via the next-generation matrix method; local and global asymptotic stability of both the disease-free equilibrium ${\mathcal{E}}_0$ (when ${\mathcal{R}}_0\le 1$) and the endemic equilibrium ${\mathcal{E}}^{*}$ (when ${\mathcal{R}}_0>1$) are established using fractional Lyapunov theory and the LaSalle invariance principle; and the normalised sensitivity indices of ${\mathcal{R}}_0$ are computed to identify transmission-amplifying and transmission-suppressing parameters. Existence, uniqueness, and Ulam–Hyers stability of solutions are established via Banach and Leray–Schauder fixed-point arguments. To complement the analytical results, a fractional physics-informed neural network ($\mathcal{PINN}$) framework is developed to simultaneously reconstruct compartmental trajectories and identify unknown biological parameters from sparse synthetic observations. $\mathcal{PINN}$ embeds the L1-Caputo discretisation directly into the training residuals and employs a four-stage Adam–L-BFGS optimisation strategy to recover five trainable parameters $\mathbf{\Theta }$ = $\{\varphi ,\mu ,\sigma ,\psi ,\beta \}$ across three fractional orders $\kappa \in \{1.0,0.95,0.9\}$. The estimated parameters show strong agreement with the true values at the classical limit $\kappa =1.0$ ($\mathrm{MAPE}=2.27\%$), with the natural mortality rate $\mu$ recovered with $\mathrm{APE}\le 0.51\%$ and the transmission rate $\beta$ with $\mathrm{APE}\le 3.63\%$ across all fractional orders, confirming the structural identifiability of the model. Pairwise correlation analysis of the learned parameters establishes the absence of equifinality, validating that $\beta$ can be reliably included in the trainable set. Noise robustness experiments under Gaussian perturbations of $1\%$, $3\%$, and $5\%$ demonstrate graceful degradation ($\mathrm{MAPE}$: $0.82\%\to 3.10\%\to 7.31\%$), confirming the reliability of the proposed framework under realistic observational conditions. Full article

This work develops a fuzzy piecewise fractional derivative (FPFD) model for cancer-immune-angiogenesis dynamics under uncertainty. Five fuzzy state variables track tumor cells, immune effectors, vessel density, oxygen, and drug concentration. We employ fuzzy triangular numbers with $\alpha$-cut interval arithmetic using constrained fuzzy arithmetic model parametric uncertainty, with numerical values. Oxygen-dependent carrying capacity follows a Hill-type function; hypoxia-induced angiogenesis follows a decreasing Michaelis–Menten function. The model transitions at $t_1=50$ days from memoryless fuzzy classical derivative to fuzzy ABC fractional derivative of order $\psi$. The transition time $t_1=50$ days is biologically justified based on experimental observations of the angiogenic switch in solid tumors, which typically occurs within 4–8 weeks post-inoculation. Positivity, boundedness, Lipschitz continuity, existence, and uniqueness of fuzzy solutions are proved via Banach fixed-point theorem in a weighted norm. A basic reproduction number interval ${\mathcal{R}}_0=[{\underline{\mathcal{R}}}_0,{\overline{\mathcal{R}}}_0]$ is derived; local and global stability conditions are established for disease-free and endemic equilibria using fuzzy differential inclusions. Global sensitivity analysis using latin hypercube sampling with $N=500$ samples explores the range of possible outcomes across the fuzzy parameter support. In the numerical implementation, we use a fourth-order fuzzy Runge–Kutta method (Phase I), and a fractional Adams–Bashforth–Moulton predictor-corrector method (Phase II), ensuring preservation of fuzzy number characteristics. Full article

This paper develops a fractional six-compartment model to describe malware spread in wireless sensor networks. To represent actual network activity, the model is constructed using generalized proportional-Caputo operators that incorporate memory and tempering effects. The existence and uniqueness of solutions are proved by applying fixed-point theorems. The stability of the system is then studied using the Ulam–Hyers approach and its extended form. A fractional Adams predictor–corrector method is employed to illustrate the dynamics. The results suggest that memory and tempering play an important role in shaping infection patterns, and they indicate that fractional calculus can provide a useful framework for studying and managing malware in distributed sensor networks. Full article

In this study, an analysis of fractional-order Lü systems is performed through a framework approach consisting of analytical solution strategies in combination with numerical methods. On the analytical methodology front, the recently developed form of the new generalized differential transform method (NGDTM) is adopted for its efficiency in providing an approximate solution with high capability in tracking the behavior of these systems. On the other hand, the Grünwald–Letnikov via Riemann–Liouville scheme (GLNS) is adopted within this study as one of its tools in confirming whether chaos exists within these systems. The performance and accuracy of the proposed method are also rigorously tested, and comparisons are made numerically with the Adams–Bashforth–Moulton method, which is used here as a standard method for validation purposes. It is clear from the results that the combination of analytical and numerical methods can greatly enhance both the speed of computation and the accuracy of results. Additionally, the proposed method or approach is found to be quite robust and accurate and can thus be employed for analyzing various fractional dynamical systems that display chaotic attractors. The proposed method can also be expanded upon in the future for analyzing complex models in science and engineering. Full article

Most existing fractional models of COVID-19 describe only the infection process without explicitly accounting for the role of vaccination. In this study, a refined Caputo fractional model is proposed that incorporates a vaccinated class to better understand how immunization influences disease progression. The mathematical formulation guarantees the existence, uniqueness, and positivity of solutions, ensuring that all system trajectories remain biologically valid. The equilibrium points are obtained, and the reproduction number is derived to identify the conditions for disease control. The stability investigation covers local behavior alongside Ulam–Hyers and its extended variants, ensuring the system remains stable under small perturbations. Numerical experiments performed with the Adams–Bashforth–Moulton algorithm illustrate that vaccination reduces infection peaks and shortens the epidemic duration. Overall, the proposed framework enriches fractional epidemiological modeling by providing deeper insight into the combined effects of memory and vaccination in controlling infectious diseases. Full article

This study presents a novel family of operators, referred to as tempered quantum fractional operators, and investigates the well-posedness of related tempered quantum fractional differential equations. The q-Adams predictor–corrector method is employed to conduct the analysis. By carefully adjusting the scheme’s parameters, the convergence rate can be controlled, while computational expenses increase linearly with time. Numerical simulations confirm the effectiveness and precision of the introduced algorithm. Full article

Fractional differential equations are used to model complex systems where present dynamics depend on past states. In this work, we study a linear fractional model with two Caputo orders that captures long-term memory together with short-term adaptation. The existence and uniqueness of solutions are established using Banach and Krasnoselskii’s fixed-point theorems. A parameter study isolates the roles of the fractional orders and coefficients, yielding an explicit stability region in the $(\alpha ,\beta )$–plane via computable contraction bounds. For computation, we implement the Adams–Bashforth–Moulton (ABM) and fractional linear multistep (FLM) methods, comparing accuracy and convergence. As an application, we model animal learning in which proficiency evolves under memory effects and pulsed stimuli. The results quantify the impact of feedback timing on trajectories within the admissible region, thereby illustrating the suitability of dual-order fractional models for memory-driven behavior. Full article

We introduce a class of triply coupled systems of differential equations with fractal–fractional Caputo derivatives and time-dependent delays. This framework captures long-memory effects and complex structural patterns while allowing delays to evolve over time, offering greater realism than constant-delay models. The existence and uniqueness of solutions are established using fixed point theory, and Hyers–Ulam stability is analyzed. A numerical scheme based on the Adams–Bashforth method is implemented to approximate solutions. The approach is illustrated through a numerical example and applied to a three-species food-chain model, comparing scenarios with and without time-dependent delays to demonstrate their impact on system dynamics. Full article

Precipitation hardening is the primary mechanism for strengthening 6xxx series aluminium alloys. The characteristics of the precipitates play a crucial role in determining the mechanical properties. In particular, predicting yield strength (YS) based on microstructure is experimentally complex and costly because its key variables, such as precipitate radius, spacing, and volume fraction (VF), are difficult to measure. Physics-based models have emerged to tackle these complications utilising advancements in simulation environments. Nevertheless, pure physics-based models require numerous free parameters and ongoing debates over governing equations. Conversely, purely data-driven models struggle with insufficient datasets and physical interpretability. Moreover, the complex dynamics between internal model variables has led both approaches to adopt heuristic optimisation methods, such as the Powell or Nelder–Mead methods, which fail to exploit valuable gradient information. To overcome these issues, we propose a gradient-based optimisation for the Kampmann–Wagner Numerical (KWN) model, incorporating CALPHAD (CALculation of PHAse Diagrams) and a strength model. Our modifications include facilitating differentiability via smoothed approximations of conditional logic, optimising non-linear combinations of free parameters, and reducing computational complexity through a single size-class assumption. Model calibration is guided by a mean squared error (MSE) loss function that aligns the YS predictions with interpolated experimental data using L2 regularisation for penalising deviations from a purely physics-based modelling structure. A comparison shows that the gradient-based adaptive moment estimation (ADAM) outperforms the gradient-free Powell and Nelder–Mead methods by converging faster, requiring fewer evaluations, and yielding more physically plausible parameters, highlighting the importance of calibration techniques in the modelling of 6xxx series precipitation hardening. 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

This article investigates modeling issues of fractional-order singular systems. The state estimation can be solved by using the particle filter. An improved Adaptive Moment Estimation (Adam) method—the Amsgrad algorithm can handle the optimization problem caused by parameter estimation. Thus, a hybrid approach that combines the particle filter and Amsgrad is proposed to estimate both parameters and states in fractional-order singular systems. This method leverages the strengths of the particle filter in handling nonlinear and high-dimensional problems, as well as the stability of the Amsgrad algorithm in optimizing parameters for dynamic systems. Then, the identification process is concluded to achieve a more accurate joint estimation. To validate the feasibility of the proposed hybrid algorithm, simulations involving three-order and four-order fractional-order singular systems are conducted. A comparative analysis with other algorithms demonstrates that the proposed method behaves better than the standard particle filter, Amsgrad and Gravitational search algorithm-Kalman filter algorithms. Full article

Despite initial changes in respiratory illness epidemiology due to SARS-CoV-2, influenza activity has returned to pre-pandemic levels, highlighting its ongoing challenges. This paper investigates an influenza epidemic model using a Susceptible-Exposed-Infected-Recovered (SEIR) framework, extended with fuzzy Atangana–Baleanu–Caputo (ABC) fractional derivatives to incorporate uncertainty (via fuzzy numbers for state variables) and memory effects (via the ABC fractional derivative for non-local dynamics). We establish the theoretical foundation by defining the fuzzy ABC derivatives and integrals based on the generalized Hukuhara difference. The existence and uniqueness of the solutions for the fuzzy fractional SEIR model are rigorously proven using fixed-point theorems. Furthermore, we analyze the system’s disease-free and endemic equilibrium points under the fractional framework. A numerical scheme based on the fractional Adams–Bashforth method is used to approximate the fuzzy solutions, providing interval-valued results for different uncertainty levels. The study demonstrates the utility of fuzzy fractional calculus in providing a more flexible and potentially realistic approach to modeling epidemic dynamics under uncertainty. Full article

To solve fractional differential equations, they are typically converted into their corresponding crisp problems through a process known as the embedding method. This paper introduces a novel direct approach to solving fuzzy differential equations using fuzzy calculations, bypassing the need for this transformation. In this study, we develop the fuzzy Adams–Bashforth (A-B) method and the fuzzy Adams–Moulton (A-M) method to find numerical solutions for fuzzy fractional differential equations (FFDEs) with fuzzy initial values. To demonstrate the accuracy and efficiency of the proposed methods, we determine both the local truncation error and the global truncation error. Additionally, we establish the convergence and stability of these methods in detail. Finally, numerical examples are provided to illustrate the flexibility and effectiveness of the proposed methods. Full article