An Operator-Based Scheme for the Numerical Integration of FDEs

An operator-based scheme for the numerical integration of fractional differential equations is presented in this paper. The generalized differential operator is used to construct the analytic solution to the corresponding characteristic ordinary differential equation in the form of an infinite power series. The approximate numerical solution is constructed by truncating the power series, and by changing the point of the expansion. The developed adaptive integration step selection strategy is based on the controlled error of approximation induced by the truncation. Computational experiments are used to demonstrate the efficacy of the proposed scheme.

The role of cytokines in the processes of adaptive integration of immune and neuroendocrine reactions of the human body

The immune, endocrine and nervous systems are integrated due to the existence of reciprocal pathways for transmitting information about changes in their actual functional state. The main task of the brain is to receive, integrate and store information, and there is strong evidence that this also applies to information obtained through the body’s immune responses. It has been proven that the production of cytokines in the brain can be caused not only by peripheral immune stimulation, but also by the nerve cells themselves, stimulated by certain neurosensory signals. Evolutionarily preserved antihomeostatic mechanisms characteristic of specific diseases are the subject of further research, the results of which may be very important for the development of therapeutic strategies that would prevent the undesirable combined effects of immune and neuroendocrine mediators.