A singular fractional Kelvin–Voigt model involving a nonlinear operator and their convergence properties

Boundary Value Problems

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[1] 0000 0000 9030 0162, grid.440761.0, School of Mathematical and Informational Sciences, Yantai University, Yantai, China;0000 0004 0375 4078, grid.1032.0, Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia;0000 0004 0369 3615, grid.453246.2, School of Science, Nanjing University of Posts and Telecommunications, Nanjing, P.R. China;0000 0004 0375 4078, grid.1032.0, Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia;0000 0004 0375 4078, grid.1032.0, Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia;0000 0001 0227 8151, grid.412638.a, School of Mathematical Sciences, Qufu Normal University, Qufu, China;0000 0004 1799 3811, grid.412508.a, Department of Mathematics, Shandong University of Science and Technology, Qingdao, China;

关键词: Uniqueness;    Nonlinear operator;    Eigenvalue problem;    Nonlocal fractional order Kelvin–Voigt model;    Singularity;    34F05;    34B16;    34L15;   

DOI  :  10.1186/s13661-019-1228-7

来源: publisher

【 摘 要 】

In this paper, we focus on a generalized singular fractional order Kelvin–Voigt model with a nonlinear operator. By using analytic techniques, the uniqueness of solution and an iterative scheme converging to the unique solution are established, which are very helpful to govern the process of the Kelvin–Voigt model. At the same time, the corresponding eigenvalue problem is studied and the property of solution for the eigenvalue problem is established. Some examples are given to illuminate the main results.

【 授权许可】

CC BY