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    On ?-Hilfer generalized proportional fractional operators
    (Amer Inst Mathematical Sciences-Aims, 2021) Mallah, Ishfaq; Ahmed, Idris; Akgul, Ali; Jarad, Fahd; Alha, Subhash
    In this paper, we introduce a generalized fractional operator in the setting of Hilfer fractional derivatives, the psi-Hilfer generalized proportional fractional derivative of a function with respect to another function. The proposed operator can be viewed as an interpolator between the Riemann-Liouville and Caputo generalized proportional fractional operators. The properties of the proposed operator are established under some classical and standard assumptions. As an application, we formulate a nonlinear fractional differential equation with a nonlocal initial condition and investigate its equivalence with Volterra integral equations, existence, and uniqueness of solutions. Finally, illustrative examples are given to demonstrate the theoretical results.