Baleanu, DumitruJajarmi, AminBaleanu, DumitruSajjadi, Samaneh SadatNieto, Juan J.Matematik2025-05-112025-05-1120220377-04271879-1778https://doi.org/10.1016/j.cam.2022.114476https://hdl.handle.net/20.500.12416/9680Jajarmi, Amin/0000-0003-2768-840XThe main purpose of this research is to present a generalization of Psi-Hilfer fractional derivative, called as regularized Psi-Hilfer, and study some of its basic characteristics. In this direction, we show that the psi-Riemann-Liouville integral is the inverse operation of the presented regularized differentiation by means of the same function psi. In addition, we consider an initial-value problem comprising this generalization and analyze the existence as well as the uniqueness of its solution. To do so, we first present an approximation sequence via a successive substitution approach; then we prove that this sequence converges uniformly to the unique solution of the regularized Psi-Hilfer fractional differential equation (FDE). To solve this FDE, we suggest an efficient numerical scheme and show its accuracy and efficacy via some real-world applications. Simulation results verify the theoretical consequences and show that the regularized Psi-Hilfer fractional mathematical system provides a more accurate model than the other kinds of integer- and fractional-order differential equations. (C) 2022 Elsevier B.V. All rights reserved.eninfo:eu-repo/semantics/closedAccessFractional DerivativeRegularized Psi-HilferExistence And UniquenessNumerical MethodArticle41510.1016/j.cam.2022.1144762-s2.0-85132587846WOS:000886910000011Q1Q1