Hyers-Ulam stability of nonlinear impulsive Volterra integro-delay dynamic system on time scales


Authors

Akbar Zada - Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan. Syed Omar Shah - Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan. Yongjin Li - Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P. R. China.


Abstract

This paper proves the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of nonlinear impulsive Volterra integro-delay dynamic system on time scales via a fixed point approach. The uniqueness and existence of the solution of nonlinear impulsive Volterra integro-delay dynamic system is proved with the help of Picard operator. The main tools for proving our results are abstract Gronwall lemma and Banach contraction principle. We also make some assumptions along with Lipschitz condition which make our results appropriate for the approach we are using.


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