TY - JOUR AU - Shah, Syed Omar AU - Zada, Akbar AU - Tunc, Cemil PY - 2019 TI - The Ulam's types stability of non-linear Volterra integro-delay dynamic system with simple non-instantaneous impulses on time scales JO - Mathematics in Natural Science SP - 13--25 VL - 4 IS - 1 AB - This manuscript presents Hyers-Ulam stability and Hyers-Ulam-Rassias stability results of non-linear Volterra integro-delay dynamic system on time scales with non-instantaneous impulses. Picard fixed point theorem is used for obtaining existence and uniqueness of solutions. By means of abstract Gronwall lemma, Gronwall's inequality on time scales and applications of Gronwall'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. SN - ISSN 2600-7665 UR - http://dx.doi.org/10.22436/mns.04.01.02 DO - 10.22436/mns.04.01.02 ID - Shah2019 ER -