In this paper, we propose the solutions of nonhomogeneous fractional integral equations of the form I03σ y(t) ++ a · I02σ y(t) ++ b · I0σ y(t) ++ c · y(t) = f (t), where I0σ+ is the Riemann–Liouville fractional integral of order σ = 1/3, 1, f (t) = tn, tn et, n ∈ N ∪ {0}, t ∈ R+, and a, b, c are constants, by using the Laplace transform technique. We obtain solutions in the form of Mellin–Ross function and of exponential function. To illustrate our findings, some examples are exhibited.
