Infinite System of Singular Integral Equations Banach Sequence Space Differential Equations of Fractional Orders
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 33, No 2-3, (2007), 241p-252p
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.