Properties for ψ-Fractional Integrals Involving a General Function ψ and Applications

In this paper, we are concerned with the psi-fractional integrals, which is a generalization of the well-known Riemann-Liouville fractional integrals and the Hadamard fractional integrals, and are useful in the study of various fractional integral equations, fractional differential equations, and fractional integrodifferential equations. Our main goal is to present some new properties for psi-fractional integrals involving a general function psi by establishing several new equalities for the psi-fractional integrals. We also give two applications of our new equalities.