Fractional Evolution Equations and Inclusions: Analysis and Control
Fractional Evolution Equations and Inclusions: Analysis and Control
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发表时间：
2016-01
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通讯作者：
Yong Zhou
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作者：
Yong Zhou
分数演化包体是非线性数学分析中微分包体的一种重要形式。它们是更广泛发展的分数进化方程（如时间分数扩散方程）的推广，是通过多元分析的视角看到的。与分数阶演化方程相比，分数阶微分包裹体理论的研究还处于起步阶段。这一点很重要，因为带有分数阶导数的微分模型为描述记忆和遗传特性提供了一个极好的工具，并且最近被证明是许多物理现象建模的有价值的工具。实际系统的分数阶模型总是比经典的整数阶模型更充分，因为当使用分数阶导数时，某些系统的描述更准确。分数衍生化的优点在模拟真实材料的力学和电学特性，描述岩石的流变特性以及其他许多领域都是显而易见的。这些模型对工程师、物理学家以及所谓的纯数学家来说都很有趣。研究干摩擦混合系统中的现象，控制传热过程，障碍问题和其他问题可以用各种微分内含物来描述，包括线性和非线性。分数进化方程和内含物是一个快速发展的研究领域，致力于分数进化方程和内含物及其在控制理论中的应用。研究了分数阶演化方程的Cauchy问题，以及带有Hille-Yosida算子的分数阶演化包含。讨论了由分数进化方程控制的系统的控制问题。最后给出了Hilbert空间中分数阶随机演化包含的研究。具有分数阶导数的微分模型为描述记忆性和遗传性提供了一个很好的工具。和他们的描述和工作将提供宝贵的见解到许多物理现象适合工程师和物理学家的建模*本书提供了必要的背景材料，需要进一步进入主题和探索丰富的研究文献
Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is however only in its initial stage of development. This is important because differential models with the fractional derivative providing an excellent instrument for the description of memory and hereditary properties, and have recently been proved valuable tools in the modeling of many physical phenomena. The fractional order models of real systems are always more adequate than the classical integer order models, since the description of some systems is more accurate when the fractional derivative is used. The advantages of fractional derivatization become evident in modeling mechanical and electrical properties of real materials, description of rheological properties of rocks and in various other fields. Such models are interesting for engineers and physicists as well as so-called pure mathematicians. Phenomena investigated in hybrid systems with dry friction, processes of controlled heat transfer, obstacle problems and others can be described with the help of various differential inclusions, both linear and nonlinear. Fractional Evolution Equations and Inclusions is devoted to a rapidly developing area of the research for fractional evolution equations & inclusions and their applications to control theory. It studies Cauchy problems for fractional evolution equations, and fractional evolution inclusions with Hille-Yosida operators. It discusses control problems for systems governed by fractional evolution equations. Finally it provides an investigation of fractional stochastic evolution inclusions in Hilbert spaces. * Systematic analysis of existence theory and topological structure of solution sets for fractional evolution inclusions and control systems* Differential models with fractional derivative provide an excellent instrument for the description of memory and hereditary properties, and their description and working will provide valuable insights into the modelling of many physical phenomena suitable for engineers and physicists* The book provides the necessary background material required to go further into the subject and explore the rich research literature