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In this work we generalize some results of the Riemann-Liouville fractional calculus for the tempered case, namely, we deal with some boundedness results of Riemann-Liouville tempered fractional integrals on continuous function space and Lebesgue spaces in bounded intervals and on the real line. Moreover, the limit behavior of the Riemann-Liouville tempered fractional integrals approaching to the Riemann-Liouville fractional integrals is considered. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate the Hardy–Littlewood type and the integration by parts result for ψ$$ \psi $$–Riemann–Liouville fractional integrals. Also, we attack the integration by parts for the ψ$$ \psi $$–Riemann–Liouville and ψ$$ \psi $$–Hilfer fractional derivatives. To finish, we investigated Sobolev‐type inequalities involving the ψ$$ \psi $$–Riemann–Liouville and the ψ$$ \psi $$–Hilfer fractional derivatives in weighted space. [ABSTRACT FROM AUTHOR]