In this study, we perform a dynamical analysis of a generalized tumor model using the Caputo fractional-order derivative. Tumor growth models are widely used in biomedical research to understand the dynamics of tumor development and to evaluate potential treatments. The Caputo fractional-order derivative is a mathematical tool that is recently being applied to model biological systems, including tumor growth. We present a detailed mathematical analysis of the generalized tumor model with the Caputo fractional-order derivative and examine its dynamical behavior. Our results show that the Caputo fractional-order derivative provides a more accurate description of the tumor growth dynamics compared to classical integer-order derivatives. We also provide a comprehensive stability analysis of the tumor model and show that the fractional-order derivative allows for a more nuanced understanding of the stability of the system. The least-square curve fitting method fits several biological parameters, including the fractional-order parameter $\alpha$. In conclusion, our study provides new insights into the dynamics of tumor growth and highlights the potential of the Caputo fractional-order derivative as a valuable tool in biomedical research. The results of this study shall have significant implications for the development of more effective treatments for tumor growth and the design of more accurate mathematical models of tumor development.

Medical imaging has experienced significant development in contemporary medicine and can now record a variety of biomedical pictures from patients to test and analyze the illness and its severity. Computer vision and artificial intelligence may outperform human diagnostic ability and uncover hidden information in biomedical images. In healthcare applications, fast prediction and reliability are of the utmost importance parameters to assure the timely detection of disease. The existing systems have poor classification accuracy, and higher computation time and the system complexity is higher. Low-quality images might impact the processing method, leading to subpar results. Furthermore, extensive preprocessing techniques are necessary for achieving accurate outcomes. Image contrast is one of the most essential visual parameters. Insufficient contrast may present many challenges for computer vision techniques. Traditional contrast adjustment techniques may not be adequate for many applications. Occasionally, these technologies create photos that lack crucial information. The primary contribution of this work is designing a Big Data Architecture (BDA) to improve the dependability of medical systems by producing real-time warnings and making precise forecasts about patient health conditions. A BDA-based Bio-Medical Image Classification (BDA-BMIC) system is designed to detect the illness of patients using Metaheuristic Optimization (Genetic Algorithm) and Gradient Approximation to improve the biomedical image classification process. Extensive tests are conducted on publicly accessible datasets to demonstrate that the suggested retrieval and categorization methods are superior to the current methods. The suggested BDA-BMIC system has average detection accuracy of 94.6% and a sensitivity of 97.3% in the simulation analysis.