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dc.contributor.authorAhmad, Irshad
dc.contributor.authorAhmad, Saeed
dc.contributor.authorur Rahman, Ghaus
dc.contributor.authorAhmad, Shabir
dc.contributor.authorDe la Sen Parte, Manuel ORCID
dc.date.accessioned2022-12-20T14:31:34Z
dc.date.available2022-12-20T14:31:34Z
dc.date.issued2022-11-26
dc.identifier.citationMathematics 10(23) : (2022) // Article ID 4466es_ES
dc.identifier.issn2227-7390
dc.identifier.urihttp://hdl.handle.net/10810/58902
dc.description.abstractRecently, several research articles have investigated the existence of solutions for dynamical systems with fractional order and their controllability. Nevertheless, very little attention has been given to the observability of such dynamical systems. In the present work, we explore the outcomes of controllability and observability regarding a differential system of fractional order with input delay. Laplace and inverse Laplace transforms, along with the Mittage–Leffler matrix function, are applied to the proposed dynamical system in Caputo’s sense, and a general solution is obtained in the form of an integral equation. Then, we set out conditions for the controllability of the underlying model, regarding the linear case. We then expound controllability conditions for the nonlinear case by utilizing the fixed point result of Schaefer and the Arzola–Ascoli theorem. Using the fixed point concept, we prove the observability of the linear case using the observability Grammian matrix. The necessary and sufficient conditions for the nonlinear case are investigated with the help of the Banach contraction mapping theorem. Finally, we add some examples to elaborate on our work.es_ES
dc.description.sponsorshipThe APC is supported by the Basque Government, Grant IT1555-22.es_ES
dc.language.isoenges_ES
dc.publisherMDPIes_ES
dc.rightsinfo:eu-repo/semantics/openAccesses_ES
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectcontrollabilityes_ES
dc.subjectobservabilityes_ES
dc.subjectgrammian matrixes_ES
dc.subjectfractional differential equationses_ES
dc.subjectfixed point theoremes_ES
dc.titleControllability and Observability Results of an Implicit Type Fractional Order Delay Dynamical Systemes_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.date.updated2022-12-09T20:23:18Z
dc.rights.holder© 2022 by the authors.Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/ 4.0/).es_ES
dc.relation.publisherversionhttps://www.mdpi.com/2227-7390/10/23/4466es_ES
dc.identifier.doi10.3390/math10234466
dc.departamentoesElectricidad y electrónica
dc.departamentoeuElektrizitatea eta elektronika


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© 2022 by the authors.Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/ 4.0/).
Except where otherwise noted, this item's license is described as © 2022 by the authors.Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/ 4.0/).