Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 17Citation - Scopus: 17Uniqueness and Existence of Positive Solutions for a Multi-Point Boundary Value Problem of Singular Fractional Differential Equations(Springeropen, 2013) Chu, Yan-Dong; Baleanu, Dumitru; Zhou, Wen-XueIn this paper, we study the uniqueness of a positive solution for the singular nonlinear fractional differential equation boundary value problem , , , , where is a real number, is the standard Riemann-Liouville differentiation and , with . Our analysis relies on a fixed-point theorem in partially ordered set. As an application, an example is presented to illustrate the main result. MSC: 26A33, 34B15, 34K37.Article Citation - WoS: 82Citation - Scopus: 89On the New Fractional Hybrid Boundary Value Problems With Three-Point Integral Hybrid Conditions(Springeropen, 2019) Etemad, S.; Pourrazi, S.; Rezapour, Sh.; Baleanu, D.We investigate some new class of hybrid type fractional differential equations and inclusions via some nonlocal three-point boundary value conditions. Also, we provide some examples to illustrate our results.Article Citation - WoS: 71Citation - Scopus: 94A Generalized Lyapunov-Type Inequality in the Frame of Conformable Derivatives(Springeropen, 2017) Abdeljawad, Thabet; Alzabut, Jehad; Jarad, FahdWe prove a generalized Lyapunov-type inequality for a conformable boundary value problem (BVP) of order alpha is an element of (1, 2]. Indeed, it is shown that if the boundary value problem (T(alpha)(c)x)(t) + r(t) x(t) = 0, t is an element of (c, d), x(c) = x(d) = 0 has a nontrivial solution, where r is a real-valued continuous function on [c, d], then integral(d)(c) vertical bar r(t)vertical bar dt > alpha(alpha)/(alpha - 1)(alpha-1) (d - c)(a-1). (1) Moreover, a Lyapunov type inequality of the form integral(d)(c)vertical bar r(t)vertical bar dt > 3 alpha - 1/(d - c)(2 alpha-1) (3 alpha - 1/2 alpha - 1)(2 alpha-1/a), 1/2 < alpha <= 1, (2) is obtained for a sequential conformable BVP. Some examples are given and an application to conformable Sturm-Liouville eigenvalue problem is analyzed.