Geodesic
Solvability of an Infinite System of Singular Integral Equations
Serdica Mathematical Journal, Tome 33 (2007) no. 2-3, pp. 241-252.

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Schauder's fixed point theorem is used to establish an existence result for an infinite system of singular integral equations in the form: (1) xi(t) = ai(t)+ ∫t0 (t − s)− α (s, x1(s), x2(s), …) ds, where i = 1,2,…, α ∈ (0,1) and t ∈ I = [0,T]. The result obtained is applied to show the solvability of an infinite system of differential equation of fractional orders.
Keywords: Infinite System of Singular Integral Equations, Banach Sequence Space, Differential Equations of Fractional Orders 
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El Borai, Mahmoud M.; Abbas, Mohamed I. Solvability of an Infinite System of Singular Integral Equations. Serdica Mathematical Journal, Tome 33 (2007) no. 2-3, pp. 241-252. http://geodesic.mathdoc.fr/item/SMJ2_2007_33_2-3_a0/