Relative controllability analysis of fractional order differential equations with multiple time delays
作者：
Highlights：
• Fractional differential systems with multiple delays are considered.
• Delayed perturbation of two parameter Mittag-Leffler type matrix function is generated for a class of multiple delay differential equations.
• Comparison between Mittag-Leffler, Delayed Mittag-Leffler and Delayed Permutation Mittag-Leffler function is given by pictorial form.
• Properties, markable remarks and continuity are presented.
• The explicit form of solution representation is constructed.
• Using Delayed Perturbation Mittag-Leffler function, the Controllability Grammian matrix is defined.
• Sufficient conditions of relative controllability are derived by using krasnoselskii’s theorem.
• Numerical illustrations were given for both linear and non-linear cases.
• Diagrammatic representations are explored using MATLAB for both linear and non-linear cases.
摘要
•Fractional differential systems with multiple delays are considered.•Delayed perturbation of two parameter Mittag-Leffler type matrix function is generated for a class of multiple delay differential equations.•Comparison between Mittag-Leffler, Delayed Mittag-Leffler and Delayed Permutation Mittag-Leffler function is given by pictorial form.•Properties, markable remarks and continuity are presented.•The explicit form of solution representation is constructed.•Using Delayed Perturbation Mittag-Leffler function, the Controllability Grammian matrix is defined.•Sufficient conditions of relative controllability are derived by using krasnoselskii’s theorem.•Numerical illustrations were given for both linear and non-linear cases.•Diagrammatic representations are explored using MATLAB for both linear and non-linear cases.
论文关键词：Caputo fractional derivative,Delayed perturbation,Mittag-Leffler functions,Relative controllability,Grammian matrix
论文评审过程：Received 10 December 2021, Revised 15 April 2022, Accepted 20 April 2022, Available online 1 May 2022, Version of Record 1 May 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127192
