Jarad, FahdOzbekler, AbdullahAbdeljawad, ThabetAgarwal, Ravi P.Alzabut, Jehad02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2018-09-122025-09-182018-09-122025-09-182018Abdeljawad, T...et al. (2018). Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives. Journal Of Inequalities Applications, 143. http://dx.doi.org/10.1186/s13660-018-1731-x1029-242Xhttps://doi.org/10.1186/s13660-018-1731-xhttps://hdl.handle.net/123456789/11622Alzabut, Prof. Dr. Jehad/0000-0002-5262-1138; Abdeljawad, Thabet/0000-0002-8889-3768; Jarad, Fahd/0000-0002-3303-0623; Agarwal, Ravi P/0000-0003-0075-1704We state and prove new generalized Lyapunov-type and Hartman-type inequalities fora conformable boundary value problem of order alpha is an element of (1,2] with mixed non-linearities of the form ((T alpha X)-X-a)(t) + r(1)(t)vertical bar X(t)vertical bar(eta-1) X(t) + r(2)(t)vertical bar x(t)vertical bar(delta-1) X(t) = g(t), t is an element of (a, b), satisfying the Dirichlet boundary conditions x(a) = x(b) = 0, where r(1), r(2), and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0 < eta < 1 < delta < 2. Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative T-alpha(a) is replaced by a sequential conformable derivative T-alpha(a) circle T-alpha(a), alpha is an element of (1/2,1]. The potential functions r(1), r(2) as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.eninfo:eu-repo/semantics/openAccessLyapunov InequalityHartman InequalityConformable DerivativeGreen'S FunctionBoundary Value ProblemMixed Non-LinearitiesArticle10.1186/s13660-018-1731-x2-s2.0-85048879028