Integrating freelance models with fractional derivatives, and artificial neural networks: A comprehensive approach to advanced computation.

In order to improve results, this work investigates how the Freelance Model (FM), Fractional Derivative (FD), and Artificial Neural Network (ANN) may all function together. We suggest a new method that combines the varied skills of freelancers with the precision of fractional derivatives and the adaptability of neural networks to maximize the benefits of each. This proposed strategy provides a new perspective to the computational methodologies and holds a promising impact on diverse industries. Future developments and applications can be made possible by this promising path toward enhanced performance in complex systems and data-driven areas. Twenty neurons have been selected and data has been trained and validated in the, following manner 70 %, 15 % and 15 %. The consistency of method has been shown using the correlation/regression and histograms in order to solve the model. The results presented here not only validate the efficacy of our approach but also open avenues for further exploration and advancements in the dynamic field of advanced computation.

Comparison of Predator-Prey Model and Hawk-Dove Game for Modelling Leukemia.

Game theory is an excellent mathematical tool to describe the interaction between the immune system and cancerous leukocytes (c.leu). The feature of cancerous leukocytes to differentiate and mutate to give rise to leukemia is in the domain of ecological models as well. In this work, the dynamic of leukemia is described and compared by two models: firstly by a simple probabilistic mathematical model using the zero-sum two player game of Hawk and Dove, and secondly by Leslie Predator Prey model of ecology. The main goal of this study is to compare the results of both models and then discuss the treatment of leukemia i.e., Hematopoietic Stem cell transplant with the best model among them. Hawk and Dove model also describes the cell to cell interaction of cancerous leukocytes and healthy leukocytes (leu) after diagnoses and the condition of the patient before and after treatments. In this work, Hematopoietic Stem cell transplant is discussed by using concepts of a zero-sum three player game. Also, both models will be characterized by determining the stability properties, identifying basins of attraction, and locating the equilibrium points to see, at what extent the patient's survival is possible with leukemia in its body. Results for both models will be presented graphically.

Does freelancing have a future? Mathematical analysis and modeling.

During the past few years, freelancing has grown exponentially due to the pandemic and subsequent economical changes in the world. In fact, in the last ten years, a drastic increase in freelancing has been observed; people quit their jobs to be their own boss. There are various reasons for this: downsizing of employees, not having fun in their jobs, unemployment, part time work to earn more, etc. Observing this vast change, many individuals on Facebook/YouTube, NGOs, and government departments started teaching freelancing as a course; to date, thousands of youngsters have been trained to start their careers as freelancers. It has been observed that the ratio of informed freelancers is more successful than those who start their careers independently. We construct a compartmental model to explore the influence of information on the expansion of freelancing in this article, which was motivated by this surge in freelancing. Following that, the model is subjected to dynamical analysis utilizing dynamical systems and differential equation theory. To validate our analytical conclusions, we used numerical simulation.