In this paper, we have presented and studied two types of the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation. We prove that the fractional order delay integral equation is Mittag-Leffler-Hyers-Ulam stable on a compact interval with respect to the Chebyshev and Bielecki norms by two notions.
We study second order nonlinear integro-differential equations in Hilbert spaces with weakly singular convolution kernels obtaining energy estimates for the solutions, uniform in t. Then we show that the solutions decay exponentially at ∞ in the energy norm. Finally, we apply these results to a problem in viscoelasticity.
We study the asymptotic behaviour of the Markov semigroup generated by an integro-partial differential equation. We give new sufficient conditions for asymptotic stability of this semigroup.