含Caputo时间分数阶导数的半线性系统的边界区域可控性

Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative

This paper investigates the regional gradient controllability for ultra-slow diffusion processes governed by the time fractional diffusion systems with a Hadamard-Caputo time fractional derivative. Some necessary and sufficient conditions on regional gradient exact and approximate controllability are first given and proved in detail. Secondly, we propose an approach on how to calculate the minimum number of $ω-$strategic actuators. Moreover, the existence, uniqueness and the concrete form of the optimal controller for the system under consideration are presented by employing the Hilbert Unique…

Regional enlarged observability of Caputo fractional differential equations

We consider the regional enlarged observability problem for fractional evolution differential equations involving Caputo derivatives. Using the Hilbert Uniqueness Method, we show that it is possible to rebuild the initial state between two prescribed functions only in an internal subregion of the whole domain. Finally, an example is provided to illustrate the theory.

Regional Controllability and Minimum Energy Control of Delayed Caputo Fractional-Order Linear Systems

We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterwards, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists in defining an attainable set, which allow us to prove exact and weak controllability. Moreover, main results include not only those of controllability but also a power…

带Caputo时间分数阶导数的分数阶微分方程的区域梯度能观性

Regional Gradient Observability for Fractional Differential Equations with Caputo Time-Fractional Derivatives

本文研究含Caputo导数的分数阶次扩散方程的区域梯度能观性，给出相关刻画与基于Hilbert Uniqueness Method的初始梯度恢复方法，数值实验验证了算法在重构误差上的有效性。

分数阶半线性系统初始状态的区域边界重构问题

The Regional Boundary Reconstruction Problem of the Initial State for Fractional Semilinear Systems

针对分数阶半线性系统，提出通过解析半群方法重构初始状态在指定边界子区域上的值，建立了区域可观测性与区域边界可观测性的联系，并给出收敛序列和数值模拟。

Riemann-Liouville分数阶半线性方程的边界可控性

Boundary Controllability of Riemann-Liouville Fractional Semilinear Equations

本文研究带Neumann边界条件的Riemann-Liouville分数阶半线性次扩散系统的边界区域可控性，利用半群理论、分数阶Hilbert唯一性方法和Schauder不动点定理给出充分条件，并通过数值模拟验证了方法的有效性。