RESUMO
In the current article, we aim to study in detail a novel coronavirus (2019-nCoV or COVID-19) mathematical model for different aspects under Caputo fractional derivative. First, from analysis point of view, existence is necessary to be investigated for any applied problem. Therefore, we used fixed point theorem's due to Banach's and Schaefer's to establish some sufficient results regarding existence and uniqueness of the solution to the proposed model. On the other hand, stability is important in respect of approximate solution, so we have developed condition sufficient for the stability of Ulam-Hyers and their different types for the considered system. In addition, the model has also been considered for semianalytical solution via Laplace Adomian decomposition method (LADM). On Matlab, by taking some real data about Pakistan, we graph the obtained results. In the last of the manuscript, a detail discussion and brief conclusion are provided.
RESUMO
BACKGROUND: Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. RESULTS: The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. CONCLUSIONS: The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis.
