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Solvability of an Infinite System of Singular Integral Equations

El Borai, Mahmoud M.Abbas, Mohamed I. — 2007

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15. 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.

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