Considering a fractional integro-differential equation involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam-Hyers stability of this problem by employing a variety of tools of fractional calculus including Banach fixed point theorem. An example is provided to illustrate our main results.
Fractional integro-differential equations $\psi$-Hilfer fractional derivative and
$\psi$-fractional integral existence uniqueness and Ulam-Hyers stability Fixed point theorem.