Controllability of a damped nonlinear fractional order integrodifferential system with input delay

Alexandria Engineering Journal

卷:61

Nawal A. Alshehri¹  S.K. Elagan²  Ghaus Ur Rahman³  Saeed Ahmad⁴  Irshad Ahmad⁴ 

[1] Corresponding author.;

[2] Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia;

[3] Department of Mathematics and Statistics, University of Swat, District Swat, Pakistan;

[4] Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan;

关键词: Fractional order differential equations;    Pantograph equation;    Grammians matrices;    Controllability;    Damped motion;   

DOI  :  

来源: DOAJ

【 摘 要 】

A novel nonlinear fractional order damped Pantographs equation involving input delay is formulated. We explored the controllability of the underlying nonlinear damped dynamical Pantograph equation of fractional order with input delay. The solution of the problem under consideration has initially expressed in the form of the Mittag–Leffler function in two different domains. The controllability Grammians matrices for both cases have been defined. Controllability in the linear case has been shown and applied Schaefer’s fixed point theorem as well as the Arzela-Ascoli theorem to derive necessary conditions for the controllability of the nonlinear case.

【 授权许可】

Unknown