Linearized Asymptotic Stability for Fractional Differential Equations

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector \{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\} where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable

APMEC: An Automated Provisioning Framework for Multi-access Edge Computing

Novel use cases and verticals such as connected cars and human-robot cooperation in the areas of 5G and Tactile Internet can significantly benefit from the flexibility and reduced latency provided by Network Function Virtualization (NFV) and Multi-Access Edge Computing (MEC). Existing frameworks managing and orchestrating MEC and NFV are either tightly coupled or completely separated. The former design is inflexible and increases the complexity of one framework. Whereas, the latter leads to inefficient use of computation resources because information are not shared. We introduce APMEC, a dedicated framework for MEC while enabling the collaboration with the management and orchestration (MANO) frameworks for NFV. The new design allows to reuse allocated network services, thus maximizing resource utilization. Measurement results have shown that APMEC can allocate up to 60% more number of network services. Being developed on top of OpenStack, APMEC is an open source project, available for collaboration and facilitating further research activities