Mallah, IshfaqAhmed, IdrisAkgul, AliJarad, FahdAlha, Subhash2024-12-242024-12-2420212473-6988https://doi.org/10.3934/math.2022005https://hdl.handle.net/20.500.12604/8371In 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.eninfo:eu-repo/semantics/openAccessHilfer fractional derivativegeneralized proportional fractional derivativeexistence and uniquenessweighed spacefixed point theoremsArticle7182102Q1WOS:00070581260000510.3934/math.2022005