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Controllability of nonlinear fractional order integrodifferential system with input delay
Author(s) -
Yi Yapeng,
Chen Diyi,
Xie Qi
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5613
Subject(s) - controllability , mathematics , nonlinear system , fixed point theorem , order (exchange) , fractional calculus , set (abstract data type) , point (geometry) , control theory (sociology) , mathematical analysis , computer science , control (management) , physics , geometry , finance , quantum mechanics , artificial intelligence , economics , programming language
This paper addressed the controllability of nonlinear fractional order integrodifferential systems with input delay. Firstly, the Caputo fractional derivatives and the Mittag‐Leffler functions are employed. Thereafter, we establish a set of sufficient and necessary conditions for the controllability of the linear fractional system. Furtherly, controllability conditions of the nonlinear integrodifferential fractional order system with input delay are acquired by utilizing Arzela‐Ascoli theorem and Schauder's fixed‐point theorem. Finally, an example is presented to demonstrate our main results.