Fractional Order Computing and Modeling with Portending Complex Fit Real-World Data

Abstract

Fractional computing models identify the states of different systems with a focus on formulating fractional order compartment models through the consideration of differential equations based on the underlying stochastic processes. Thus, a systematic approach to address and ensure predictive accuracy allows that the model remains physically reasonable at all times, providing a convenient interpretation and feasible design regarding all the parameters of the model. Towards these manifolding processes, this study aims to introduce new concepts of fractional calculus that manifest crossover effects in dynamical models. Piecewise global fractional derivatives in sense of Caputo and Atangana-Baleanu-Caputo (ABC) have been utilized, and they are applied to formulate the Zika Virus (ZV) disease model. To have a predictive analysis of the behavior of the model, the domain is subsequently split into two subintervals and the piecewise behavior is investigated. Afterwards, the fixed point theory of Schauder and Banach is benefited from to prove the existence and uniqueness of at least one solution in both senses for the considered problem. As for the numerical simulations as per the data, Newton interpolation formula has been modified and extended for the considered nonlinear system. Finally, graphical presentations and illustrative examples based on the data for various compartments of the systems have been presented with respect to the applicable real-world data for different fractional orders. Based on the impact of fractional order reducing the abrupt changes, the results obtained from the study demonstrate and also validate that increasing the fractional order brings about a greater crossover effect, which is obvious from the observed data, which is critical for the effective management and control of abrupt changes like infectious diseases, viruses, among many more unexpected phenomena in chaotic, uncertain and transient circumstances.