Volume 6, Issue 4, August 2018, Page: 135-141
Formulation of Impulsive Differential Equations with Time-Dependent Continuous Delay
Ita Micah Esuabana, Department of Mathematics, Faculty of Science, University of Calabar, Calabar, Nigeria
Ubon Akpan Abasiekwere, Department of Mathematics and Statistics, Faculty of Science, University of Uyo, Uyo, Nigeria
Received: Sep. 10, 2018;       Accepted: Oct. 9, 2018;       Published: Oct. 31, 2018
DOI: 10.11648/j.ajam.20180604.11      View  175      Downloads  16
Abstract
Research in impulsive delay differential equations has been undergoing some exciting growth in recent times. This to a large extent can be attributed to the quest by mathematicians in particular and the science community as a whole to unveil nature the way it truly is. The realization that differential equations, in general, and indeed impulsive delay differential equations are very important models for describing the true state of several real-life processes/phenomena may have been the tunic. One can attest that in most human processes or natural phenomena, the present state is most often affected significantly by their past state and those that were thought of as continuous may indeed undergo abrupt change at several points or even be stochastic. In this study, a special strictly ascending continuous delay is constructed for a class of system of impulsive differential equations. It is demonstrated that even though the dynamics of the system and the delay have ideal continuity properties, the right side may not even have limits at some points due to the impact of past impulses in the present. The integral equivalence of the formulated system of equations is also obtained via a scheme similar to that of Perron by making use of certain assumptions.
Keywords
Impulsive, Differential Equation, Continuous Delay, Integral Equivalence
To cite this article
Ita Micah Esuabana, Ubon Akpan Abasiekwere, Formulation of Impulsive Differential Equations with Time-Dependent Continuous Delay, American Journal of Applied Mathematics. Vol. 6, No. 4, 2018, pp. 135-141. doi: 10.11648/j.ajam.20180604.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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