Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 10Citation - Scopus: 8Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems(Hindawi Ltd, 2013) Mohammadzadeh, B.; Neamaty, A.; Baleanu, D.; Darzi, R.; Bleanu, D.We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem D(0+)(alpha)u(t) + f(t, u(t)) = 0, 0 < t < 1, 2 < alpha <= 3, u(0) = u'(0) = 0, D-0(alpha-1),u(1) = beta u(xi), 0 < xi < 1, where D-0+(alpha) denotes Riemann-Liouville fractional derivative, beta is positive real number, beta xi(alpha-1) >= 2 Gamma(alpha), and f is continuous on [0, 1] x [0,infinity). As an application, one example is given to illustrate the main result.Article Citation - WoS: 15Citation - Scopus: 18Existence of a Periodic Mild Solution for a Nonlinear Fractional Differential Equation(Pergamon-elsevier Science Ltd, 2012) Baleanu, Dumitru; Herzallah, Mohamed A. E.; Mohammadzadeh, B.; Darzi, R.; Neamaty, A.The aim of this manuscript is to analyze the existence of a periodic mild solution to the problem of the following nonlinear fractional differential equation (R)(0)D(t)(alpha)u(t) - lambda u(t) = f(t, u(t)), u(0) = u(1) = 0, 1 < alpha < 2, lambda is an element of R, where D-R(0)t(alpha), denotes the Riemann-Liouville fractional derivative. We obtained the expressions of the general solution for the linear fractional differential equation by making use of the Laplace and inverse Laplace transforms. By making use of the Banach contraction mapping principle and the Schaefer fixed point theorem, the existence results of one or at least one mild solution for a nonlinear fractional differential equation were given. (C) 2011 Elsevier Ltd. All rights reserved.