Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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.Article Citation - WoS: 41Citation - Scopus: 44Fractional Euler-Lagrange Equations Revisited(Springer, 2012) Baleanu, Dumitru; Herzallah, Mohamed A. E.This paper presents the necessary and sufficient optimality conditions for the Euler-Lagrange fractional equations of fractional variational problems with determining in which spaces the functional must exist where the functional contains right and left fractional derivatives in the Riemann-Liouville sense and the upper bound of integration less than the upper bound of the interval of the fractional derivative. In order to illustrate our results, one example is presented.Article Citation - WoS: 70Citation - Scopus: 80Fractional-Order Euler-Lagrange Equations and Formulation of Hamiltonian Equations(Springer, 2009) Baleanu, Dumitru; Herzallah, Mohamed A. E.This paper presents the fractional order Euler-Lagrange equations and the transversality conditions for fractional variational problems with fractional integral and fractional derivatives defined in the sense of Caputo and Riemann-Liouville. A fractional Hamiltonian formulation was developed and some illustrative examples were treated in detail.