5,456 research outputs found
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
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
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