ON \(\psi\) FRACTIONAL INTEGRAL

The \(\psi\) $\psi$ fractional integral is a product of the combination of Riemann-Liouville fractional integral and Stieltjes integral. The integral transforms including Laplace transform and Mellin transform for this fractional integral are introduced. The mapping properties of \(\psi\) $\psi$ fractional integral are mentioned. The reason that the condition of \(\psi (t)\rightarrow +\infty\) $\psi (t)\to +\infty$ as \(t\rightarrow +\infty\) $t\to +\infty$ must be imposed in the definitions of \(\psi\) $\psi$ fractional integral and derivatives is explained when they are applied to \(\psi\) $\psi$ fractional differential equations.