Application of piecewise fractional differential equation to COVID-19 infection dynamics

Fredholm boundary-value problem for the system of fractional differential equations

This paper deals with the study of Fredholm boundary-value problem for the system of fractional differential equations with Caputo derivative. The boundary-value problem is specified by linear vector functional such that the number of it components does not coincide with the dimension of the system of fractional differential equations. We first considered the general solution of the system of fractional differential equations that consist with the general solution of the associated homogeneous system and the arbitrary particular solution of the inhomogeneous system. The particular solution we found is a solution of the system of linear Volterra integral equations of the second kind with weakly singular kernels. Further, by using the theory of pseudo-inverse matrices, we established conditions that should be imposed on the coefficients of the original problem to guarantee that the indicated boundary conditions are satisfied. Moreover, a family of linearly independent solutions of this boundary-value problem is constructed. The specific examples are provided to verify the effectiveness of the proposed approach.

Research Software vs. Research Data I: Towards a Research Data definition in the Open Science context

Background: Research Software is a concept that has been only recently clarified. In this paper we address the need for a similar enlightenment concerning the Research Data concept. Methods: Our contribution begins by reviewing the Research Software definition, which includes the analysis of software as a legal concept, followed by the study of its production in the research environment and within the Open Science framework. Then we explore the challenges of a data definition and some of the Research Data definitions proposed in the literature. Results: We propose a Research Data concept featuring three characteristics: the data should be produced (collected, processed, analyzed, shared & disseminated) to answer a scientific question, by a scientific team, and has yield a result published or disseminated in some article or scientific contribution of any kind. Conclusions: The analysis of this definition and the context in which it is proposed provides some answers to the Borgman's conundrum challenges, that is, which Research Data might be shared, by whom, with whom, under what conditions, why, and to what effects. They are completed with answers to the questions: how? and where?