Alzabut, JehadAbdeljawad, ThabetJarad, FahdSudsutad, Weerawat2020-01-132020-01-132019Alzabut, Jehad...et al. (2019). "A Gronwall inequality via the generalized proportional fractional derivative with applications", Journal of Inequalities and Applications.1029-242Xhttp://hdl.handle.net/20.500.12416/2334In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its features. As an application, we accommodate the newly defined derivative to prove the uniqueness and obtain a bound in terms of Mittag-Leffler function for the solutions of a nonlinear delay proportional fractional system. An example is presented to demonstrate the applicability of the theory.eninfo:eu-repo/semantics/openAccessProportional Gronwall InequalityUniqueness of SolutionDelay Proportional Fractional SystemBound For the SolutionArticle10.1186/s13660-019-2052-4