Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions
Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions
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DOI：
10.1515/fca-2015-0007
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发表时间：
2014-09
影响因子：
3
通讯作者：
A. Debbouche;Delfim F. M. Torres
中科院分区：
文献类型：
--
作者：
A. Debbouche;Delfim F. M. Torres
摘要：我们证明了Banach 空间中Sobolev 型分数非局部动力学方程温和解的存在性和唯一性。索博列夫非局部条件根据黎曼-刘维尔分数阶导数来考虑。考虑拉格朗日最优控制问题，并得到多重积分解的存在性。主要工具包括分数阶微积分、半群理论、算子分数次方、格朗沃尔不等式的奇异版本以及 Leray-Schauder 不动点定理。给出了一个说明该理论的例子。
Abstract In We prove existence and uniqueness of mild solutions to Sobolev type fractional nonlocal dynamic equations in Banach spaces. The Sobolev nonlocal condition is considered in terms of a Riemann-Liouville fractional derivative. A Lagrange optimal control problem is considered, and existence of a multi-integral solution obtained. Main tools include fractional calculus, semigroup theory, fractional power of operators, a singular version of Gronwall's inequality, and Leray-Schauder fixed point theorem. An example illustrating the theory is given.