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Nasrin Eghbali, Vida Kalvandi, John M. Rassias (2016)
Open Mathematics
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.
Jung, Soon-Mo (2007)
Fixed Point Theory and Applications [electronic only]
Buşe, Constantin, Jitianu, Oprea (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Piermarco Cannarsa, Daniela Sforza (2008)
Applicationes Mathematicae
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.
Choulli, M. (1991)
Journal of Applied Mathematics and Stochastic Analysis
El-Sayed, M.A. (1994)
International Journal of Mathematics and Mathematical Sciences
El-Doma, M. (2004)
Journal of Applied Mathematics
William E. Fitzgibbon (1988)
Czechoslovak Mathematical Journal
Katarzyna Pichór (1998)
Annales Polonici Mathematici
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.
Danuta Jama (1986)
Annales Polonici Mathematici
Kaim, Sebastian J. (2007)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
Igor Brilla (1984)
Aplikace matematiky
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.
Reynolds, David W., Appleby, John A.D. (2008)
Electronic Journal of Probability [electronic only]
Darwish, Mohamed, Henderson, Johnny (2009)
Fractional Calculus and Applied Analysis
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.
Domoshnitsky, Alexander, Goltser, Yakov (2000)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Gachpazan, Mortaza, Baghani, Omid (2010)
Fixed Point Theory and Applications [electronic only]
Castro, L.P., Ramos, A. (2008)
Banach Journal of Mathematical Analysis [electronic only]
Gaetano Fichera (1990)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
— 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....
Wang, Tingxiu (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
S. Askhabov (1991)
Colloquium Mathematicae
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