Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Editorial Advanced Theoretical and Applied Studies of Fractional Differential Equations 2013(Hindawi Publishing Corporation, 2014) Baleanu, Dumitru; Trujillo, Juan J.; Ahmad, BashirCorrection Citation - WoS: 12Common Fixed Point Theorems in Modified Intuitionistic Fuzzy Metric Spaces (Vol 2013, 189321, 2013)(Hindawi Publishing Corporation, 2014) Manro, Saurabh; Kumar, Sanjay; Bhatia, S. S.; Tas, KenanArticle On fractional order hybrid differential equations(Hindawi Publishing Corporation, 2014) Herzallah, Mohamed A. E.; Baleanu, DumitruWe develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0 << 1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.Article Citation - WoS: 11Citation - Scopus: 79Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets Within Local Fractional Operators(Hindawi Publishing Corporation, 2014) Tenreiro Machado, J. A.; Cattani, Carlo; Baleanu, Mihaela Cristina; Yang, Xiao-Jun; Baleanu, DumitruWe perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.Editorial Citation - WoS: 2Citation - Scopus: 3Fractional and Time-Scales Differential Equations(Hindawi Publishing Corporation, 2014) Torres, Delfim F. M.; Bhrawy, Ali H.; Salahshour, Soheil; Baleanu, DumitruArticle Citation - WoS: 10Citation - Scopus: 11The Existence of Solution for a K-Dimensional System of Multiterm Fractional Integrodifferential Equations With Antiperiodic Boundary Value Problems(Hindawi Publishing Corporation, 2014) Nazemi, Sayyedeh Zahra; Rezapour, Shahram; Baleanu, DumitruThere are many published papers about fractional integrodifferential equations and system of fractional differential equations. The goal of this paper is to show that we can investigate more complicated ones by using an appropriate basic theory. In this way, we prove the existence and uniqueness of solution for k-dimensional system of multiterm fractional integrodifferential equations with antiperiodic boundary conditions by applying some standard fixed point results. An illustrative example is also presented.Article Citation - WoS: 61Citation - Scopus: 73On Fractional Order Hybrid Differential Equations(Hindawi Publishing Corporation, 2014) Baleanu, Dumitru; Herzallah, Mohamed A. E.We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0 < alpha < 1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.Article Citation - WoS: 8Citation - Scopus: 13A New Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions(Hindawi Publishing Corporation, 2014) Liu, Sanyang; Baleanu, Dumitru; Zhang, Lihong; Wang, GuotaoA new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented.Article Citation - WoS: 26Citation - Scopus: 32Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations(Hindawi Publishing Corporation, 2012) Mohammadi, H.; Rezapour, Sh.; Baleanu, D.We investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problem D(0+)(alpha)u(t) + D(0+)(beta)u(t) = f(t, u(t)), u(0) = 0, 0 < t < 1, where 0 < beta < alpha < 1, D-0+(alpha) is the standard Riemann-Liouville differentiation and f : [0,1] x [0,infinity) -> [0,infinity) is continuous. By using some fixed-point results on cones, some existence and multiplicity results of positive solutions are obtained.Article Citation - WoS: 42Citation - Scopus: 41The Q-Fractional Analogue for Gronwall-Type Inequality(Hindawi Publishing Corporation, 2013) Abdeljawad, Thabet; Alzabut, Jehad O.We utilize q-fractional Caputo initial value problems of order 0 < alpha <= 1 to derive a.. -analogue for Gronwall-type inequality. Some particular cases are derived where q-Mittag-Leffler functions and q-exponential type functions are used. An example is given to illustrate the validity of the derived inequality.