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.
In this paper the author studies existence and bifurcation of a nonlinear homogeneous Volterra integral equation, which is derived as the first approximation for the solution of the time dependent generalization of the von Kármán equations. The last system serves as a model for stability (instability) of a thin rectangular visco-elastic plate whose two opposite edges are subjected to a constant loading which depends on the parameters of proportionality of this boundary loading.
Mathematics Subject Classification: 45G10, 45M99, 47H09We study the solvability of a perturbed quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions which are defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions. Finally, we give an example to illustrate our abstract results.
— Si mostra come la scelta di una topologia nello spazio delle funzioni ammissibili, in taluni problemi, influenzi i relativi risultati. Vengono mostrati tre esempi. Due tratti dall'Analisi matematica pura: uno riguardante la stabilità della soluzione di un'equazione integrale di Volterra e l'altro il problema di Cauchy per l'equazione di Laplace come «problema ben posto». Il terzo esempio è relativo alla Fisica matematica, precisamente al «Principio della Memoria evanescente» in Viscoelasticità....