Ahmed, IdrisAkgul, AliJarad, FahdAlha, SubhashMallah, Ishfaq02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2022-11-102025-09-182022-11-102025-09-182021Mallah, Ishfaq...et al. (2021). "On psi-Hilfer generalized proportional fractional operators", AIMS Mathematics, Vol. 7, No. 1, pp. 82-102.2473-6988https://doi.org/10.3934/math.2022005https://hdl.handle.net/123456789/11871In 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 TheoremsArticle10.3934/math.2022005