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

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 exp...

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Bibliographic Details
Published inAlexandria engineering journal Vol. 61; no. 3; pp. 1956 - 1966
Main Authors Ahmad, Irshad, Rahman, Ghaus Ur, Ahmad, Saeed, Alshehri, Nawal A., Elagan, S.K.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2022
Elsevier
Subjects
Controllability
Damped motion
Fractional order differential equations
Grammians matrices
Pantograph equation
Grammians matrices
Controllability
Damped motion
Fractional order differential equations
Pantograph equation
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Summary: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.
ISSN:1110-0168
DOI:10.1016/j.aej.2021.06.081