Abdeljawad, ThabetJarad, FahdMallak, Saed F.Alzabut, Jehad2020-02-172020-02-172019Abdeljawad, Thabet...et al. (2019). "Lyapunov type inequalities via fractional proportional derivatives and application on the free zero disc of Kilbas-Saigo generalized Mittag-Leffler functions", European Physical Journal Plus, Vol. 134, No. 5.2190-5444http://hdl.handle.net/20.500.12416/2458In this article, we prove Lyapunov type inequalities for a nonlocal fractional derivative, called fractional proportional derivative, generated by modified conformable or proportional derivatives in both Riemann-Liuoville and Caputo senses. Further, in the Riemann-Liuoville case we prove a Lyapunov inequality for a fractional proportional weighted boundary value problem and apply it on a weighted Sturm-Liouville problem to estimate an upper bound for the free zero disk of the Kilbas-Saigo Mittag-Leffler functions of three parameters. The proven results generalize and modify previously obtained results in the literature.eninfo:eu-repo/semantics/closedAccessDifferential-EquationsStability AnalysisArticle134510.1140/epjp/i2019-12772-1