Browsing by Author "Eid, Rajeh"

Now showing 1 - 7 of 7

Citation Count: 55
Applications of the extended fractional Euler-Lagrange equations model to freely oscillating dynamical systems
(Publishing House of the Romanian Academy, 2016) Agila,A.; Baleanu,D.; Eid,R.; Irfanoglu,B.; Department of Mechatronics Engineering; Mathematics
The fractional calculus and the calculus of variations are utilized to model and control complex dynamical systems. Those systems are presented more accurately by means of fractional models. In this study, an extended version of the fractional Euler-Lagrange equations is introduced. In these equations the damping force term is extended to be proportional to the fractional derivative of the displacement with variable fractional order. The finite difference methods and the Coimbra fractional derivative are used to approximate the solution of the introduced fractional Euler-Lagrange equations model. The free oscillating single pendulum system is investigated. © 2016, Editura Academiei Romane. All rights reserved.
Citation Count: 48
APPLICATIONS OF THE EXTENDED FRACTIONAL EULER-LAGRANGE EQUATIONS MODEL TO FREELY OSCILLATING DYNAMICAL SYSTEMS
(Editura Acad Romane, 2016) Agila, Adel; Baleanu, Dumitru; Eid, Rajeh; Irfanoglu, Bulent; Department of Mechatronics Engineering; Mathematics
The fractional calculus and the calculus of variations are utilized to model and control complex dynamical systems. Those systems are presented more accurately by means of fractional models. In this study, an extended version of the fractional Euler-Lagrange equations is introduced. In these equations the damping force term is extended to be proportional to the fractional derivative of the displacement with variable fractional order. The finite difference methods and the Coimbra fractional derivative are used to approximate the solution of the introduced fractional Euler-Lagrange equations model. The free oscillating single pendulum system is investigated.
Citation Count: 17
Development of Decision Support Model for Selecting a Maintenance Plan Using a Fuzzy MCDM Approach: A Theoretical Framework
(Hindawi Ltd, 2018) Abdulgader, Fathia Sghayer; Eid, Rajeh; Rouyendegh (B Erdebilli), Babak Daneshvar; Mathematics; Computer Engineering
In complex decision making, using multicriteria decision-making (MCDM) methodologies is the most scientific way to ensure an informed and justified decision between several alternatives. MCDMs have been used in different ways and with several applications that proved their efficiency in achieving this goal. In this research, the advantages and disadvantages of the different MCDM methodologies are studied, along with the different techniques implemented to increase their accuracy and precision. The main aim of the study is to develop a hybrid MCDM process that combines the strengths of several MCDM methods and apply it to choose the best fit maintenance policy/strategy for industrial application. Moreover, fuzzy linguistic terms are utilized in all of the used MCDM techniques in order to eliminate the uncertainty and ambiguity of the results. Through an extensive literature review performed on studies that have used MCDM methods in a hybrid context and using fuzzy linguistic terms, a model is developed to use fuzzy DEMATEL-AHP-TOPSIS hybrid technique. The model with its application is the first of its kind, which combines the strengths of fuzzy DEMATEL in establishing interrelationships between several criteria, as well as performing a pairwise comparison between the criteria for prioritization using the fuzzy AHP method. Thereafter, the alternatives are compared using fuzzy TOPSIS method by establishing negative and positive solutions and calculating the relative closeness for each of the alternatives. Furthermore, six main criteria, twenty criteria, and five alternatives are selected from the literature for the model application.
Citation Count: 21
Fractional dimensional harmonic oscillator
(2011) Eid,R.; Muslih,S.I.; Baleanu,D.; Rabei,E.; Mathematics
The fractional Schrödinger equation corresponding to the fractional oscillator was investigated. The regular singular points and the exact solutions of the corresponding radial Schrödinger equation were reported.
Citation Count: 11
A freely damped oscillating fractional dynamic system modeled by fractional Euler-Lagrange equations
(Sage Publications Ltd, 2018) Agila, Adel; Baleanu, Dumitru; Eid, Rajeh; Irfanoglu, Bulent; Mathematics; Department of Mechatronics Engineering
The behaviors of some vibrating dynamic systems cannot be modeled precisely by means of integer representation models. Fractional representation looks like it is more accurate to model such systems. In this study, the fractional Euler-Lagrange equations model is introduced to model a fractional damped oscillating system. In this model, the fractional inertia force and the fractional damping force are proportional to the fractional derivative of the displacement. The fractional derivative orders in both forces are considered to be variable fractional orders. A numerical approximation technique is utilized to obtain the system responses. The discretization of the Coimbra fractional derivative and the finite difference technique are used to accomplish this approximation. The response of the system is verified by a comparison to a classical integer representation and is obtained based on different values of system parameters.
Citation Count: 49
On fractional Schrodinger equation in α-dimensional fractional space
(Pergamon-elsevier Science Ltd, 2009) Eid, Rajeh; Muslih, Sami I.; Baleanu, Dumitru; Rabei, E.; Mathematics
The Schrodinger equation is solved in a-dimensional fractional space with a Coulomb potential proportional to 1/r(beta-2), 2 <= beta <= 4. The wave functions are studied in terms of spatial dimensionality alpha and beta and the results for beta = 3 are compared with those obtained in the literature. (C) 2008 Elsevier Ltd. All rights reserved.
Poısson denkleminin sonlu elemanlar çözümü
(2019) Mohammed, Taha Yousıf Mohammed; Eid, Rajeh; Mathematics
Bu tez çalışmasında Sonlu elemanlar yöntemi (FEM) iki boyutlu (2D) poisson denklemini çözmek için uygulanmıştır.([8]). Algoritmamızı oluşturmak için şekil fonksiyonu kullandık. Bu çalışmada kullandığımız şekil fonksiyonları, doğrusal ve ikinci dereceden interpolasyon fonksiyonları olarak seçilmiştir([2],[9]). Doğrusal şekil fonksiyonunu 3 düğümlü üçgen, ve 4 düğümlü dikdörtgen elemanlara uygularken, ikinci dereceden fonksiyon 6 düğümlü üçgen ve dikdörtgen elemanlara uygulanmıştır. Daha sonra incelenen problemin yaklaşık çözümünü hesaplamak için sonlu elemanlar metodunu uyguladık. Çözümün doğruluğunu göstermek için lineer ve kuadratik şekil fonksiyonları kullanılarak sayısal sonuçlar elde edilmiştir. Çözümün verimliliği, Sonlu elemanlar yöntemi kullanılarak bulunan sonuçların, tam çözümle karşılaştırılarak gözlemlenmiştir.