Abstract
We present the conditions under which every positive solution x of the integral equation x ( t ) = a ( t ) + ∫ c t ( t − s ) α − 1 k ( t , s ) f ( s , x ( s ) ) d s , c > 1 , α > 0 satisfies x ( t ) = O ( a ( t ) ) as t → ∞ , i.e. , lim sup t → ∞ x ( t ) a ( t ) < ∞ . From the obtained results, we derive a technique which can be applied to some related integral equations that are equivalent to certain fractional differential equations of Caputo derivative of any order.
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