Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Towards a reference model for SOA governance (extended version)

Although the lack of elaborate governance mechanisms is often seen as the main reason for failures of SOA projects, SOA governance is still very low in maturity. In this paper, we follow a design science approach to address this drawback by presenting a framework that can guide organisations in implementing a governance approach for SOA more successfully. We have reviewed the highly advanced IT governance frameworks Cobit and ITIL and mapped them to the SOA domain. The resulting blueprint for an SOA governance framework was refined based on a detailed literature review, expert interviews and a practical application in a government organisation. The proposed framework stresses the need for business representatives to get involved in SOA decisions and to define benefits ownership for services.