Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 103Citation - Scopus: 114On Coupled Systems of Time-Fractional Differential Problems by Using a New Fractional Derivative(Hindawi Ltd, 2016) Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; Alsaedi, AhmedThe existence of solutions for a coupled system of time-fractional differential equations including continuous functions and the Caputo-Fabrizio fractional derivative is examined. After that we investigated a coupled system of time-fractional differential inclusions including compact-and convex-valued L-1-Caratheodory multifunctions and the Caputo-Fabrizio fractional derivative.Article Citation - WoS: 257Analysis of Time-Fractional Hunter-Saxton Equation: a Model of Neumatic Liquid Crystal(Sciendo, 2016) Baleanu, Dumitru; Alsaedi, Ahmed; Atangana, AbdonIn this work, a theoretical study of diffusion of neumatic liquid crystals was done using the concept of fractional order derivative. This version of fractional derivative is very easy to handle and obey to almost all the properties satisfied by the conventional Newtonian concept of derivative. The mathematical equation underpinning this physical phenomenon was solved analytically via the so-called homotopy decomposition method. In order to show the accuracy of this iteration method, we constructed a Hilbert space in which we proved its stability for the time-fractional Hunder-Saxton equation.Article Citation - WoS: 443New Properties of Conformable Derivative(de Gruyter Poland Sp Zoo, 2015) Baleanu, Dumitru; Alsaedi, Ahmed; Atangana, AbdonRecently, the conformable derivative and its properties have been introduced. In this work we have investigated in more detail some new properties of this derivative and we have proved some useful related theorems. Also, some new definitions have been introduced.Article On coupled systems of time-fractional differential problems by using a new fractional derivative(Hindawi Publishing Corporation, 2016) Alsaedi, Ahmed; Baleanu, Dumitru; Etemad, Sina; Rezapour, ShahramThe existence of solutions for a coupled system of time-fractional differential equations including continuous functions and the Caputo-Fabrizio fractional derivative is examined. After that we investigated a coupled system of time-fractional differential inclusions including compact-and convex-valued L-1-Caratheodory multifunctions and the Caputo-Fabrizio fractional derivative.Article Citation - WoS: 121Citation - Scopus: 132A Novel Expansion Iterative Method for Solving Linear Partial Differential Equations of Fractional Order(Elsevier Science inc, 2015) Abu Arqub, Omar; Momani, Shaher; Baleanu, Dumitru; Alsaedi, Ahmed; El-Ajou, AhmadIn this manuscript, we implement a relatively new analytic iterative technique for solving time-space-fractional linear partial differential equations subject to given constraints conditions based on the generalized Taylor series formula. The solution methodology is based on generating the multiple fractional power series expansion solution in the form of a rapidly convergent series with minimum size of calculations. This method can be used as an alternative to obtain analytic solutions of different types of fractional linear partial differential equations applied in mathematics, physics, and engineering. Some numerical test applications were analyzed to illustrate the procedure and to confirm the performance of the proposed method in order to show its potentiality, generality, and accuracy for solving such equations with different constraints conditions. Numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the suggested algorithm. (C) 2015 Elsevier Inc. All rights reserved.Article Citation - WoS: 29Citation - Scopus: 31On a Time-Fractional Integrodifferential Equation Via Three-Point Boundary Value Conditions(Hindawi Ltd, 2015) Rezapour, Shahram; Etemad, Sina; Alsaedi, Ahmed; Baleanu, DumitruThe existence and the uniqueness theorems play a crucial role prior to finding the numerical solutions of the fractional differential equations describing the models corresponding to the real world applications. In this paper, we study the existence of solutions for a time-fractional integrodifferential equation via three-point boundary value conditions.