Hyers-Ulam Stability of Non-Linear Volterra Integro-Delay Dynamic System with Fractional Integrable Impulses on Time Scales

Authors

A. Zada Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

S. O. Shah Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

Abstract:

This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem is used for obtaining existence and uniqueness of solutions. By means of abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish Hyers-Ulam stability and Hyers-Ulam-Rassias stability results. There are some primary lemmas, inequalities and relevant assumptions that helps in our stability results.

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