Fen - Edebiyat Fakültesi

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A Computationally Efficient Method For a Class of Fractional Variational and Optimal Control Problems Using Fractional Gegenbauer Functions
(Editura Academiei Romane, 2018) Baleanu, Dumitru; Doha, Eid H.; Ezz-Eldien, Samer S.; Abdelkawy, M. A.; Hafez, R. M.; Amin, A. Z. M.; Baleanu, Dumitru; Zaky, M. A.; 56389; Matematik
This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.
A Discussion On the Role of People in Global Software Development [Rasprava O Ulozi Ljudi U Globalnom Razvoju Softvera]
(2013) Pusatlı, Özgür Tolga; Colomo-Palacios, Ricardo; Pusatlı, Özgür Tolga; Soto-Acosta, Pedro; 51704; Yönetim Bilişim Sistemleri
Literature is producing a considerable amount of papers which focus on the risks, challenges and solutions of global software development (GSD). However, the influence of human factors on the success of GSD projects requires further study. The aim of our paper is twofold. First, to identify the challenges related to the human factors in GSD and, second, to propose the solution(s), which could help in solving or reducing the overall impact of these challenges. The main conclusions of this research can be valuable to organizations that are willing to achieve the quality objectives regarding GSD projects.
A Gap in the Paper A Note On Cone Metric Fixed Point Theory and Its Equivalence [Nonlinear Anal. 72(5), (2010), 2259-2261]
(2011) Abdeljawad, Thabet; Karapınar, Erdal; Matematik
There is a gap in Theorem 2.2 of the paper of Du [1]. In this paper, we shall state the gap and repair it.
A modified Laplace transform for certain generalized fractional operators
(2018) Jarad, Fahd; Thabet, Abdeljawad; 234808; Matematik
It is known that Laplace transform converges for functions of exponential order. In order to extend the possibility of working in a large class of functions, we present a modified Laplace transform that we call ρ-Laplace transform, study its properties and prove its own convolution theorem. Then, we apply it to solve some ordinary differential equations in the frame of a certain type generalized fractional derivatives. This modified transform acts as a powerful tool in handling the kernels of these generalized fractional operators
A New Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions
(Hindawi LTD, 2014) Baleanu, Dumitru; Liu, Sanyang; Zhang, Lihong; Baleanu, Dumitru; 56389; Matematik
A 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.
A Note On (P, Q)-Analogue Type of Fubini Numbers and Polynomials
(American Institute of Mathematical Sciences, 2020) Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389; Matematik
In this paper, we introduce a new class of (p, q)-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for (p, q)-Fubini polynomials associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials and (p, q)-Stirling numbers of the second kind.
A Note On Non-İnstantaneous Impulsive Fractional Neutral Integro-Differential Systems With State-Dependent Delay in Banach Spaces
(Eudoxus Press, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Kalamani, Palaniyappan; Arjunan, M. Mallika; 56389; Matematik
In this research, we establish the existence results for non-instantaneous impulsive fractional neutral integro-differential systems with state-dependent delay in Banach space. By utilizing the Banach contraction principle and condensing fixed point theorem coupled with semigroup theory, we build up the desired results. To acquire the main results, our working concepts are that the functions deciding the equation fulfill certain Lipschitz conditions of local type which is similar to the hypotheses [5]. In the end, an example is given to show the abstract theory.
A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems
(Sage Publications LTD, 2017) Baleanu, Dumitru; Doha, E. H.; Baleanu, Dumitru; Bhrawy, A. H.; 56389; Matematik
The numerical solution of a fractional optimal control problem having a quadratic performance index is proposed and analyzed. The performance index of the fractional optimal control problem is considered as a function of both the state and the control variables. The dynamic constraint is expressed as a fractional differential equation that includes an integer derivative in addition to the fractional derivative. The order of the fractional derivative is taken as less than one and described in the Caputo sense. Based on the shifted Legendre orthonormal polynomials, we employ the operational matrix of fractional derivatives, the Legendre-Gauss quadrature formula and the Lagrange multiplier method for reducing such a problem into a problem consisting of solving a system of algebraic equations. The convergence of the proposed method is analyzed. For confirming the validity and accuracy of the proposed numerical method, a numerical example is presented along with a comparison between our numerical results and those obtained using the Legendre spectral-collocation method.
A Result On A Pata-Ciric Type Contraction At A Point
(MDPI AG, 2020) Karapınar, Erdal; Fulga, Andreea; Rakoˇcevi´c, Vladimir; 19184; Matematik
In this manuscript, we define a new contraction mapping, Pata-Cirictype contraction at a point, that merges distinct contractions defined by Seghal, Pata and Ciric. We proved that in a complete space, each Pata-Cirictype contraction at a point possesses a fixed point. We express an example to illustrate the observed result.
About Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
(Amer Soc Mechanical Engineers, 2005) Baleanu, Dumitru; Muslih, Sami I.; 56389; Matematik
sRecently, an extension of the simplest fractional problem and the fractional variational problem of Lagrange was obtained by Agrawal. The first part of this study presents the fractional Lagrangian formulation of mechanical systems and introduce the Levy path integral. The second part is an extension to Agrawal's approach to classical fields with fractional derivatives. The classical fields with fractional derivatives are investigated by using the Lagrangian formulation. The case of the fractional Schrodinger equation is presented.
About Some New Developments in Fractional Variational Principles
(10th International Conference on Non-Integer Calculus and Its Applications (RRNR2018), 2018) Defterli, Özlem; 31401; Matematik
About the F-N Approximation to Fractional Neutron Transport Equation in Slab Geometry
(Amer Soc Mechanical Engineers, 2012) Baleanu, Dumitru; Kadem, Abdelouahab; 56389; Matematik
The neutron transport denotes the study of the motions and interactions of neutrons with materials. In given applications we need to know where neutrons are in an apparatus, what direction they are moving, and how fast they are going. In this manuscript the Legendre polynomial approximation method F-N was applied to the one dimensional slab geometry neutron transport equation.
Advanced Regression Models for Complex Regulatory Systems with Applications: CMARS versus MARS
(American Institute of Mathematical Science, 2018) Özlem, Defterli; Özmen, Ayşe; 31401
Mathematical models are important not only to provide a better understanding for the underlying dynamics of huge systems, whose components are highly correlated, but also enables us to interpret their future behavior and compare with other possible situations. In this respect, there is a crucial demand for efficient new approaches to infer such complex phenomena which may appear in real-world problems of the fields like system biology, medicine, engineering, finance, education, environment and so on. In such systems, the components appear in a high dimensional network structure where they are interconnected with each other and under the effect of some unknown external parameters needed to be identified. In this study, we implement conic multivariate adaptive regression spline (CMARS) technique on a real-world data from system biology for the inference of such complex regulatory networks. The performance of the model is investigated in comparison with the results obtained from multivariate adaptive regression spline (MARS) modeling approach.
Analysis of the model of HIV-1 infection of CD4(+) T-cell with a new approach of fractional derivative
(2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389; Matematik
By using the fractional Caputo-Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.
Analysis of the new technique to solution of fractional wave- and heat-like equation
(Jagiellonian Univ Press, 2017) Baleanu, Dumitru; Agheli, Bahram; Darzi, Rahmat; 56389; Matematik
We have applied the new approach of homotopic perturbation method (NHPM) for wave- and heat-like equation featuring time-fractional derivative. A combination of NHPM and multiple fractional power series form has been used the first time to present analytical solution. In order to illustrate the simplicity and ability of the suggested approach, some specific and clear examples have been given. All computations were done using Mathematica.
Analytical Approximate Solutions of (N + 1)-Dimensional Fractal Heat-Like and Wave-Like Equations
(MDPI AG, 2017) Baleanu, Dumitru; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas; 56389; Matematik
In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.
Article shape effect of nanosize particles on magnetohydrodynamic nanofluid flow and heat transfer over a stretching sheet with entropy generation
(2020) Baleanu, Dumitru; Baleanu, Dumitru; Iqbal, Azhar; Abbas, Muhammd; 56389; Matematik
Magnetohydrodynamic nanofluid technologies are emerging in several areas including pharmacology, medicine and lubrication (smart tribology). The present study discusses the heat transfer and entropy generation of magnetohydrodynamic (MHD) Ag-water nanofluid flow over a stretching sheet with the effect of nanoparticles shape. Three different geometries of nanoparticles—sphere, blade and lamina—are considered. The problem is modeled in the form of momentum, energy and entropy equations. The homotopy analysis method (HAM) is used to find the analytical solution of momentum, energy and entropy equations. The variations of velocity profile, temperature profile, Nusselt number and entropy generation with the influences of physical parameters are discussed in graphical form. The results show that the performance of lamina-shaped nanoparticles is better in temperature distribution, heat transfer and enhancement of the entropy generation.
Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations
(2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; 56389; Matematik
We establish the long-time asymptotic formula of solutions to the (1+α)-order fractional differential equation 0iOt1+αx+a(t)x=0, t>0, under some simple restrictions on the functional coefficient a(t), where 0iOt1+α is one of the fractional differential operators 0Dtα(x′), (0Dtαx)′= 0Dt1+αx and 0Dtα(tx′-x). Here, 0Dtα designates the Riemann-Liouville derivative of order α∈(0,1). The asymptotic formula reads as [b+O(1)] ·xsmall+c·xlarge as t→+∞ for given b, c∈R, where xsmall and xlarge represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation 0iOt1+αx=0, t>0
Coincidence and Fixed Points of Non-expansive Type Mappings on 2-Metric Spaces
(2007) Taş, Kenan; Dubey, Sweetee; Taş, Kenan; 4971; Matematik
In this paper a unique coincidence value is obtained for a class of self mappings satisfying non-expansive type condition on 2-metric spaces under various conditions and a fixed point theorem is also obtained.
Combined Optical Solitary Waves and Conservation Laws For Nonlinear Chen-Lee-Liu Equation in Optical Fibers
(Elsevier GMBH, Urban & Fischer Verlag, 2018) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389; Matematik
This paper obtains a combined optical solitary wave solution that is modeled by nonlinear Chen-Lee-Liu equation (NCLE) which arises in the context of temporal pulses along optical fibers associated with the self-steepening nonlinearity using the complex envelope function ansatz. The novel combined solitary wave describes bright and dark solitary wave properties in the same expression. The intensity and the nonlinear phase shift of the combined solitary wave solution are reported. Moreover, the Lie point symmetry generators or vector fields of a system of partial differential equations (PDEs) which is acquired by transforming the NCLE to a real and imaginary parts are derived. It is observed that the obtained system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conservation laws (Cis) for the system using the general Cls theorem. Numerical simulation and physical interpretations of the obtained results are demonstrated with interesting figures showing the meaning of the acquired results. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the NCLE. (C) 2017 Elsevier GmbH. All rights reserved.

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