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Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation

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.

Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters

Shu-Gui Kang, Bao Shi, Sui Sun Cheng (2009)

Annales Polonici Mathematici

Existence of periodic solutions of functional differential equations with parameters such as Nicholson’s blowflies model call for the investigation of integral equations with parameters defined over spaces with periodic structures. In this paper, we study one such equation ϕ ( x ) = λ [ x , x + ω ] Ω K ( x , y ) h ( y ) f ( y , ϕ ( y - τ ( y ) ) ) d y , x ∈ Ω, by means of the proper value theory of operators in Banach spaces with cones. Existence, uniqueness and continuous dependence of proper solutions are established.

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