Integro-differential operators with non-singular kernels have been much discussed among fractional calculus researchers. We present a mathematical study to clearly establish the rigorous foundations of this topic. By considering function spaces and mapping results, we show that can be defined on larger than singular kernels, as differentiability conditions removed. also discover an analogue Son...

In this paper we derive the sharp long time stability and error estimates of nite element approximations for parabolic integro di erential equations First the exponential decay of the solution as t is studied and then the semi discrete and fully discrete approximations are considered using the Ritz Volterra projection Other related problems are studied as well The main feature of our analysis i...

in which ak'S and bk'S are complex constants,fk(x) represents the kth derivative of the unknown function f(x) with prescribed initial valuesfk(0), along with the conditions thatfk(oo) = 0, for k = 0, 1, 2 . . . . . n, and 9(x) represents a known differentiable function arises in a natural way while solving a class of mixed boundary value problems of mathematical physics (see [-3, 5, 6]). Varley...

Due to the plentiful dynamical behaviors, integro-differential equations with delays have many applications in a variety of fields such as control theory, biology, ecology, medicine, etc [1, 2]. Especially, the effects of delays on the stability of integro-differential equations have been extensively studied in the previous literature (see [3]-[9] and references cited therein). Besides delays, ...