Currently, it’s far widely recognized reality that fractional evaluation is an enticing area of study, particularly in modeling. This paper discusses the proposed fractional derivatives for the dynamical transmission of the Coronavirus model with the Mittag-Leffler kernel. These are the latest techniques that give useful results in analyzing and controlling COVID-19 infection in the community. Moreover, several strategies, such as fixed-point theory, linear growth, and Ulam-Hyres stability of the suggested operator, have been applied to the fractional order model. To see the effects of the model, we employ the Sumudu transform and an effective method as well. The PID and Controllability of the model is also discussed. Lastly, by creating a computational framework that integrates the stochastic technique of artificial neural networks with Levenberg-Marquardt backpropagation (ANNLMB), we provide the numerical calculations of the suggested model in four distinct variations. The model’s tools are powerful and capable of modelling theoretical conditions. They are also suggested for application in other physical models of infectious diseases.
A nonlinear three-species predator-prey model containing populations of prey, intermediate predators, and top predators was proposed and examined. To represent more realistic prey growth and saturation mechanisms inherent in ecological systems, the model incorporates exponential functional responses and restricted prey growth. The model’s qualitative dynamics are examined using equilibrium and local stability analysis, and the population time evolution is numerically examined using the Forward Euler and fourth-order Runge-Kutta (RK4) method. Numerical simulations are used to examine the coexistence behavior, oscillatory dynamics, and asymptotic stability over a long enough period of time. After all, the system tends to a stable coexistence equilibrium since the time-series profiles and phase pictures show that the overall population is positive and bounded under suitable parameter values. The numerical results further demonstrate that the nonlinear trophic interactions between the species cause the species to naturally display transitory oscillations. Furthermore, the results show that the RK4 schemes are more numerically stable than the Euler scheme, especially for larger simulation time steps and smaller error tolerances. Analyzes of parameter sensitivity are also carried out in relation to the intrinsic prey growth rate. The findings demonstrate that, although the species continue to coexist over time, oscillatory behavior is stronger and population fluctuations are larger when the prey growth parameter is higher. The incorporation of restricted prey growth with exponential predator response in a tri-trophic ecological framework and a thorough comparison of traditional numerical techniques for stability and convergence analysis are the innovative aspects of this work. The suggested model advances the mathematical understanding of multispecies population dynamics and provides insightful information on the nonlinear interactions among ecological processes. Furthermore, an artificial neural network (ANN) is used to assess the numerical solutions of the model and learn the numerical adjustment between the RK4 and Euler approximations. The ANN accurately replicates the RK4 time-series and phase-space trajectories, achieving one-step prediction errors of order 10 -7 .
Baboons in Saudi Arabia’s Al Baha province frequently interact with people, creating crossspecies transmission settings that classical, integer-order epidemic models cannot reproduce. By utilizing the Caputo-Fabrizio fractional operator, we are able to encode history effects via a nonsingular kernel over two hosts with nonlocal memory. Memory strength determines outbreak magnitude, decay rates, and oscillatory patterns across a range of fractional indices. It can precipitate a variety of complex and chaotic transients absent from the integer-order limit. Mathematically, we establish Ulam-Hyers stability for the proposed dynamic, ensuring solution robustness under small perturbations and modelling noise. The resulting methodology offers a principled tool for designing public-health actions and wildlife management policies in regions with sustained human-wildlife interfaces.
In this paper, we investigate the [Formula: see text]-dimensional non-linear porous medium equation under the [Formula: see text]-Hilfer derivative. A comprehensive qualitative analysis of the solution is presented, including existence, uniqueness, and Ulam-Hyers (UH) stability. Moreover, for the numerical simulations, a linearized quadrature method (LQM) is developed for the proposed model. MATLAB numerical simulations comprise two- and three-dimensional plots, which demonstrate how changes in the fractional order [Formula: see text] and type parameter [Formula: see text] influence the dynamics of the solutions. The neural network approach demonstrates excellent predictive capability, accurately capturing the behaviour of the model with high precision. This work advances both the theory and computation of the high-dimensional porous medium flows under the [Formula: see text]-Hilfer derivative.
Skin cancer, particularly melanoma, remains a critical global health challenge where early detection significantly improves patient survival and reduces healthcare costs. In response to this need, this study presents a deep learning–based approach to transforming skin cancer diagnosis through accessible, accurate automated detection. A convolutional neural network (CNN) architecture with YOLO11 was developed and evaluated to improve melanoma classification in dermatological images. To further enhance diagnostic reliability, an image preprocessing stage was implemented to remove artifacts such as hair, thereby improving overall image quality and classification performance. The proposed model achieved 90% accuracy, with strong sensitivity and specificity, demonstrating its effectiveness in distinguishing benign from malignant lesions. Beyond technical performance, this work highlights the potential of CNN to expand access to early melanoma detection, particularly in resource-limited settings where specialist care may be scarce. By enabling faster, more cost-effective, and more reliable screening, this approach helps reduce diagnostic delays, optimize healthcare resources, and ultimately improve patient outcomes and quality of life. These results support the continued development of AI-driven tools as scalable solutions for equitable and impactful healthcare delivery.
