Umarov Sabir, Ashurov Ravshan, Chen YangQuan
Department of Mathematics, University of New Haven, 300 Boston Post Road, West Haven, CT 06516 USA.
Institute of Mathematics, Academy of Sciences of Republic of Uzbekistan, Tashkent, Uzbekistan.
Fract Calc Appl Anal. 2021;24(1):254-277. doi: 10.1515/fca-2021-0011. Epub 2021 Jan 29.
This paper is devoted to the general theory of linear systems of fractional order pseudo-differential equations. Single fractional order differential and pseudo-differential equations are studied by many authors and several monographs and handbooks have been published devoted to its theory and applications. However, the state of systems of fractional order ordinary and partial or pseudo-differential equations is still far from completeness, even in the linear case. In this paper we develop a new method of solution of general systems of fractional order linear pseudo-differential equations and prove existence and uniqueness theorems in the special classes of distributions, as well as in the Sobolev spaces.
本文致力于分数阶伪微分方程线性系统的一般理论。许多作者研究了单个分数阶微分方程和伪微分方程，并且已经出版了几本专著和手册来论述其理论和应用。然而，即使在线性情况下，分数阶常微分方程、偏微分方程或伪微分方程系统的研究现状仍远未完善。在本文中，我们开发了一种求解分数阶线性伪微分方程一般系统的新方法，并证明了在特殊分布类以及索伯列夫空间中的存在性和唯一性定理。
