Some boundedness results for \(\psi \)-Riemann–Liouville and \(\psi \)-Riemann–Liouville tempered fractional integrals in \({\mathbb {R}}\)

In this paper, using Hardy–Littlewood maximal function, we deal with the boundedness of the \(\psi \)-Riemann–Liouville in Lebesgue and weighted Lebesgue space in the real line. Moreover, we consider the boundedness of \(\psi \)-Riemann–Liouville tempered fractional integrals in weighted Lebesgue space in the real line.