We apply the Kurzweil-Henstock integral setting to prove a Fredholm Alternative-type result for the integral equation
x (t) – K∫[a, b]α (t, s) x (s) ds = ƒ (t), t ∈ [a, b],
where x and ƒ are Kurzweil integrable functions (possibly highly oscillating) defined on a compact interval [a, b] of the real line with values on Banach spaces. An application is given.
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