| Abstract |
In this paper, we propose the solutions of non-homogeneous fractional integral equations of the form
$${I_{0^+}^{2\sigma}}y(t)+a\cdot {I_{0^+}^{\sigma}}y(t)+b\cdot y(t)=t^n,$$
and
$${I_{0^+}^{2\sigma}}y(t)+a\cdot {I_{0^+}^{\sigma}}y(t)+b\cdot y(t)=t^ne^t,$$
where ${I_{0^+}^{\sigma}}$ is the Riemann-Liouville fractional integral of order $\sigma =1/2, \sigma=1, n\in \mathbb{N} \cup \{0\}, t\in \mathbb{R}^+,$ and $a,b$ are constants, by using the Laplace transform technique. We obtain the solutions of these equations are in the form of Mellin-Ross function and in the form of exponential function. |
Publication
Journal Publication
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