{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T08:22:15Z","timestamp":1772785335146,"version":"3.50.1"},"reference-count":45,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2020,5,8]],"date-time":"2020-05-08T00:00:00Z","timestamp":1588896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,3,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this work, we investigate the controllability results of a fractional integro-differential equation with non-instantaneous impulses on time scales. Banach contraction theorem and the non-linear functional analysis have been used to establish these results. In support, a numerical example with simulation for different time scales is given to validate the obtained analytical outcomes.<\/jats:p>","DOI":"10.1093\/imamci\/dnaa008","type":"journal-article","created":{"date-parts":[[2020,4,2]],"date-time":"2020-04-02T11:16:27Z","timestamp":1585826187000},"page":"211-231","source":"Crossref","is-referenced-by-count":21,"title":["Controllability results of fractional integro-differential equation with non-instantaneous impulses on time scales"],"prefix":"10.1093","volume":"38","author":[{"given":"Vipin","family":"Kumar","sequence":"first","affiliation":[{"name":"School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, 175075 Himachal Pradesh, India"}]},{"given":"Muslim","family":"Malik","sequence":"additional","affiliation":[{"name":"School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, 175075 Himachal Pradesh, India"}]}],"member":"286","published-online":{"date-parts":[[2020,5,8]]},"reference":[{"key":"2021021910075663400_ref1","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1007\/s10440-008-9356-6","article-title":"A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions","volume":"109","author":"Agarwal","year":"2010","journal-title":"Acta Appl. Math."},{"key":"2021021910075663400_ref2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/BF03322019","article-title":"Basic calculus on time scales and some of its applications","volume":"35","author":"Agarwal","year":"1999","journal-title":"Results Math."},{"key":"2021021910075663400_ref3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0377-0427(01)00432-0","article-title":"Dynamic equations on time scales: a survey","volume":"141","author":"Agarwal","year":"2002","journal-title":"J. Comput. Appl. Math."},{"key":"2021021910075663400_ref4","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.nahs.2009.01.008","article-title":"Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations. Nonlinear Anal","volume":"3","author":"Ahmad","year":"2009","journal-title":"Hybrid Syst."},{"key":"2021021910075663400_ref5","first-page":"241","article-title":"On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales","volume":"38","author":"Ahmadkhanlu","year":"2012","journal-title":"Bull. Iranian Math. Soc."},{"key":"2021021910075663400_ref6","first-page":"1","article-title":"Fractional derivatives and integrals on time scales via the inverse generalized Laplace transform","volume":"11","author":"Bastos","year":"2011","journal-title":"Int. J. Math. Comput."},{"key":"2021021910075663400_ref7","doi-asserted-by":"crossref","DOI":"10.1155\/9789775945501","volume-title":"Impulsive Differential Equations and Inclusions","author":"Benchohra","year":"2006"},{"key":"2021021910075663400_ref8","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.sigpro.2014.05.026","article-title":"A fractional calculus on arbitrary time scales: fractional differentiation and fractional integration","volume":"107","author":"Benkhettou","year":"2015","journal-title":"Signal Process."},{"key":"2021021910075663400_ref9","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.jksus.2015.08.001","article-title":"Existence and uniqueness of solution for a fractional Riemann\u2013Liouville initial value problem on time scales","volume":"28","author":"Benkhettou","year":"2016","journal-title":"J. King Saud. Univ. Sci."},{"key":"2021021910075663400_ref10","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.jksus.2015.05.003","article-title":"A conformable fractional calculus on arbitrary time scales","volume":"28","author":"Benkhettou","year":"2016","journal-title":"J. King Saud. Univ. Sci."},{"key":"2021021910075663400_ref11","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0201-1","volume-title":"Dynamic Equations on Time Scales","author":"Bohner","year":"2001"},{"key":"2021021910075663400_ref12","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-8176-8230-9","volume-title":"Advances in Dynamic Equations on Time Scales","author":"Bohner","year":"2003"},{"key":"2021021910075663400_ref13","doi-asserted-by":"crossref","first-page":"149","DOI":"10.21136\/MB.2012.142861","article-title":"Controllability and observability of time-invariant linear dynamic systems","volume":"137","author":"Bohner","year":"2012","journal-title":"Math. Bohem."},{"key":"2021021910075663400_ref14","first-page":"1","article-title":"Controllability, observability, realizability and stability of dynamic linear systems","volume":"2009","author":"Davis","year":"2009","journal-title":"Electron. J. Differential Equations"},{"key":"2021021910075663400_ref15","doi-asserted-by":"crossref","first-page":"1442","DOI":"10.1016\/j.camwa.2011.03.075","article-title":"Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems","volume":"62","author":"Debbouche","year":"2011","journal-title":"Comput. Math. Appl."},{"key":"2021021910075663400_ref16","doi-asserted-by":"crossref","first-page":"1577","DOI":"10.1080\/00207179.2013.791927","article-title":"Approximate controllability of fractional nonlocal delay semilinear systems in Hilbert spaces","volume":"86","author":"Debbouche","year":"2013","journal-title":"Internat. J. Control."},{"key":"2021021910075663400_ref17","first-page":"161","article-title":"Approximate controllability of fractional delay dynamic inclusions with nonlocal control conditions","volume":"243","author":"Debbouche","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"2021021910075663400_ref18","first-page":"70","article-title":"Controllability of semilinear dynamic systems on time scales","volume":"8","author":"Duque","year":"2017","journal-title":"J. Abstr. Differ. Equ. Appl."},{"key":"2021021910075663400_ref19","doi-asserted-by":"crossref","first-page":"1641","DOI":"10.1090\/S0002-9939-2012-11613-2","article-title":"On a new class of abstract impulsive differential equations","volume":"141","author":"Hern\u00e1ndez","year":"2013","journal-title":"Proc. Amer. Math. Soc."},{"key":"2021021910075663400_ref20","article-title":"Ein Ma$\\beta $kettenkalk\u00fcl mit Anwendung auf Zentrumsmannigfaltigkeiten","author":"Hilger","year":"1998"},{"key":"2021021910075663400_ref21","doi-asserted-by":"crossref","first-page":"61","DOI":"10.4067\/S0719-06462019000100061","article-title":"On fractional integro-differential equations with state-dependent delay and non-instantaneous impulses","volume":"21","author":"Khalida","year":"2019","journal-title":"Cubo"},{"key":"2021021910075663400_ref22","first-page":"73","article-title":"Existence of solutions to a new class of abstract non-instantaneous impulsive fractional integro-differential equations","volume":"16","author":"Kumar","year":"2016","journal-title":"Nonlinear Dyn. Syst. Theory."},{"key":"2021021910075663400_ref23","doi-asserted-by":"crossref","DOI":"10.1142\/0906","volume-title":"Theory of Impulsive Differential Equations","author":"Lakshmikantham","year":"1989"},{"key":"2021021910075663400_ref24","doi-asserted-by":"crossref","first-page":"2677","DOI":"10.1016\/j.na.2007.08.042","article-title":"Basic theory of fractional differential equations","volume":"69","author":"Lakshmikantham","year":"2008","journal-title":"Nonlinear Anal."},{"key":"2021021910075663400_ref25","doi-asserted-by":"crossref","first-page":"2803","DOI":"10.1016\/j.na.2007.08.052","article-title":"A class of the first order impulsive dynamic equations on time scales","volume":"69","author":"Liu","year":"2008","journal-title":"Nonlinear Anal."},{"key":"2021021910075663400_ref26","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1016\/j.mcm.2011.04.001","article-title":"On controllability and observability for a class of linear impulsive dynamic systems on time scales","volume":"54","author":"Lupulescu","year":"2011","journal-title":"Math. Comput. Model."},{"key":"2021021910075663400_ref27","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1002\/asjc.1604","article-title":"Controllability of fractional differential equation of order $\\alpha \\in (1, 2]$ with non-instantaneous impulses","volume":"20","author":"Malik","year":"2018","journal-title":"Asian J. Control."},{"key":"2021021910075663400_ref28","first-page":"197","article-title":"Periodic solutions to second order non-linear differential equation with non-instantaneous impulses","volume":"26","author":"Malik","year":"2017","journal-title":"Dyn. Syst. App."},{"key":"2021021910075663400_ref29","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.jksus.2016.11.005","article-title":"Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses","volume":"30","author":"Malik","year":"2018","journal-title":"J. King Saud. Univ. Sci."},{"key":"2021021910075663400_ref30","article-title":"Controllability of neutral differential equation with impulses on time scales. Differ. Equ","volume":"2019","author":"Malik","year":"2019","journal-title":"Dyn. Syst."},{"key":"2021021910075663400_ref31","first-page":"276","article-title":"Existence, stability and controllability results of a Volterra integro-dynamic system with non-instantaneous impulses on time scales","volume":"37","author":"Malik","year":"2019","journal-title":"IMA J. Math. Control Inform."},{"key":"2021021910075663400_ref32","doi-asserted-by":"crossref","first-page":"3489","DOI":"10.1140\/epjst\/e2018-00036-0","article-title":"Generalized fractional operators on time scales with application to dynamic equations","volume":"226","author":"Mekhalfi","year":"2017","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"2021021910075663400_ref33","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"Miller","year":"1993"},{"key":"2021021910075663400_ref34","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1093\/imamci\/dny011","article-title":"Controllability of semilinear impulsive control systems with multiple time delays in control","volume":"36","author":"Muni","year":"2018","journal-title":"IMA J. Math. Control Inform."},{"key":"2021021910075663400_ref35","volume-title":"Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications","author":"Podlubny","year":"1998"},{"key":"2021021910075663400_ref36","first-page":"333","article-title":"On controllability of nonlinear impulsive integrodifferential systems","volume":"15","author":"Sakthivel","year":"2008","journal-title":"Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal."},{"key":"2021021910075663400_ref37","article-title":"Controllability criteria of fractional differential dynamical systems with non-instantaneous impulses","author":"Vadivoo","year":"2019","journal-title":"IMA J. Math. Control Inform."},{"key":"2021021910075663400_ref38","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1093\/imamci\/dnx048","article-title":"Controllability for a class of second order functional evolution differential equations without uniqueness","volume":"36","author":"Vijayakumar","year":"2017","journal-title":"IMA J. Math. Control Inform."},{"key":"2021021910075663400_ref39","first-page":"915","article-title":"A general class of impulsive evolution equations","volume":"46","author":"Wang","year":"2015","journal-title":"Topol. Methods Nonlinear Anal."},{"key":"2021021910075663400_ref40","doi-asserted-by":"crossref","DOI":"10.1088\/2053-2563\/aada21","volume-title":"Non-Instantaneous Impulsive Differential Equations Basic Theory and Computation","author":"Wang","year":"2018"},{"key":"2021021910075663400_ref41","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1093\/imamci\/dnx055","article-title":"Controllability of fractional non-instantaneous impulsive differential inclusions without compactness","volume":"36","author":"Wang","year":"2017","journal-title":"IMA J. Math. Control Inform."},{"key":"2021021910075663400_ref42","doi-asserted-by":"crossref","first-page":"3642","DOI":"10.1016\/j.nonrwa.2011.06.021","article-title":"Existence and controllability results for fractional semilinear differential inclusions","volume":"12","author":"Wang","year":"2011","journal-title":"Nonlinear Anal."},{"key":"2021021910075663400_ref43","doi-asserted-by":"crossref","first-page":"4346","DOI":"10.1016\/j.cnsns.2012.02.029","article-title":"Complete controllability of fractional evolution systems","volume":"17","author":"Wang","year":"2012","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"2021021910075663400_ref44","first-page":"247","article-title":"Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales","volume":"42","author":"Yan","year":"2016","journal-title":"Bull. Iranian Math. 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