Stability analysis of linear Volterra equations on time scales under bounded perturbations

Abstract

We analyze the stability of the zero solution to Volterra equations on time scales with respect to two classes of bounded perturbations. We obtain sufficient conditions on the kernel which include some known results for continuous and for discrete equations. In order to check the applicability of these conditions, we apply the theory to a test example

A Qualitative Study on Fractional Logistic Integro-differential Equations in an Arbitrary Time Scale

“…Different problems in engineering and natural phenomenons are extensively modelled into fractional equations. See, for example [13,16,17,27,28,[33][34][35]38] and references cited therein. Over the past few years different researchers have qualitatively studied fractional integro-differential equations and time scales integro-differential equations separately, see [1,4,5,11,12,21,32] and references cited therein.…”

Nabla inequalities and permanence for a logistic integrodifferential equation on time scales

“…For example, it can model insect populations that are continuous while in season (and may follow a di erence scheme with variable step-size), die out in winter, while their eggs are incubating or dormant, and then hatch in a new season, giving rise to a nonoverlapping population. The study of population dynamic systems on time scales can reveal new qualitative phenomenon, see, for example, [2][3][4][5][6][7][8].…”