Fen - Edebiyat Fakültesi

Permanent URI for this communityhttps://hdl.handle.net/20.500.12416/1

Browse

Now showing 1 - 20 of 412

A caputo fractional order boundary value problem with integral boundary conditions
(Eudoxus Press, 2013) Abdeljawad, Thabet; Abdeljawad, Thabet
In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. The nonlinear alternative of the Leray- Schauder type Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution under certain conditions. The compactness of solutions set is also investigated and an example is included to show the applicability of our results.
A chebyshev-laguerre-gauss-radau collocation scheme for solving a time fractional sub-diffusion equation on a semi-infinite domain
(The Publishing House of the Romanian Academy, 2015) Baleanu, Dumitru; Abdelkawy, M. A.; Alzahrani, A. A.; Baleanu, Dumitru; Alzahrani, Ebraheem
We propose a new efficient spectral collocation method for solving a time fractional sub-diffusion equation on a semi-infinite domain. The shifted Chebyshev-Gauss-Radau interpolation method is adapted for time discretization along with the Laguerre-Gauss-Radau collocation scheme that is used for space discretization on a semi-infinite domain. The main advantage of the proposed approach is that a spectral method is implemented for both time and space discretizations, which allows us to present a new efficient algorithm for solving time fractional sub-diffusion equations
A common fixed point theorem of a Gregus type on convex cone metric spaces
(Eudoxus Press, 2011) Abdeljawad, Thabet; Karapınar, Erdal; 19184
The result of Ciric [1] on a common fixed point theorem of Gregus-type on metric spaces is extended to the class of cone metric spaces. Namely, a common fixed point theorem is proved in s-convex cone metric spaces under the normality of the cone and another common fixed point theorem is proved in convex cone metric spaces under the assumption that the cone is strongly minihedral
A discussion on the role of people in global software development
(Univ Osijek, Tech Fac., 2013) Misra, Sanjay; Colomo-Palacios, Ricardo; Pusatlı, Tolga; Soto-Acosta, Pedro; 51704
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 fite type result for sequental fractional differintial equations
(Dynamic Publisher, 2010) Abdeljawad, Thabet; Baleanu, Dumitru; Jarad, Fahd; Mustafa, Octavian G.; Trujillo, J. J.
Given the solution f of the sequential fractional differential equation aD(t)(alpha)(aD(t)(alpha) f) + P(t)f = 0, t is an element of [b, a], where -infinity < a < b < c < + infinity, alpha is an element of (1/2, 1) and P : [a, + infinity) -> [0, P(infinity)], P(infinity) < + infinity, is continuous. Assume that there exist t(1),t(2) is an element of [b, c] such that f(t(1)) = (aD(t)(alpha))(t(2)) = 0. Then, we establish here a positive lower bound for c - a which depends solely on alpha, P(infinity). Such a result might be useful in discussing disconjugate fractional differential equations and fractional interpolation, similarly to the case of (integer order) ordinary differential equations
A fractional derivative inclusion problem via an integral boundary condition
(Eudoxus Press, 2016) Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram
We investigate the existence of solutions for the fractional differential inclusion (c)D(alpha)x(t) is an element of F(t, x(t)) (equipped with the boundary value problems x(0) = 0 and x(1) = integral(eta)(0) x(s)ds, where 0 < eta < 1, 1 < alpha <= 2, D-c(alpha) is the standard Caputo differentiation and F : [0, 1] x R -> 2(R) is a compact valued multifunction. An illustrative example is also discussed.
A fractional Dirac equation and its solution
(IOP Publishing LTD, 2010) Baleanu, Dumitru; Agrawal, Om. P.; Baleanu, Dumitru
This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order a. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit a. 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics
A fractional finite difference inclusion
(Eudoxus Press, 2016) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid
In this manuscript we investigated the fractional finite difference inclusion Delta(mu)(mu-2) x(t) is an element of F(t, x(t), Delta x(t)) via the boundary conditions Delta x(b + mu) = A and x(mu - 2) = B, where 1 <= 2, A,B is an element of R and F :N-mu-2(b+mu+2) x R -> 2(R) is a compact valued multifunction.
A fractional schrödinger equation and its solution
(Springer/Plenum Publishers, 2010) Baleanu, Dumitru; Baleanu, Dumitru; Agrawal, Om. P.
This paper presents a fractional Schrodinger equation and its solution. The fractional Schrodinger equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives to obtain the fractional Euler-Lagrange equations of motion. We present the Lagrangian for the fractional Schrodinger equation of order alpha. We also use a fractional Klein-Gordon equation to obtain the fractional Schrodinger equation which is the same as that obtained using the fractional variational principle. As an example, we consider the eigensolutions of a particle in an infinite potential well. The solutions are obtained in terms of the sines of the Mittag-Leffler function
A generalized contraction principle with control functions on partial metric spaces
(Pergamon-Elsevier Science Ltd, 2012) Abdeljawad, Thabet; Karapınar, Erdal; Taş, Kenan; 19184; 4971
Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions phi and psi on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions
A generalized Lyapunov-type inequality in the frame of conformable derivatives
(Springer, 2017) Abdeljawad, Thabet; Alzabut, Jehad; Jarad, Fahd; 234808
We prove a generalized Lyapunov-type inequality for a conformable boundary value problem (BVP) of order alpha is an element of (1, 2]. Indeed, it is shown that if the boundary value problem (T(alpha)(c)x)(t) + r(t) x(t) = 0, t is an element of (c, d), x(c) = x(d) = 0 has a nontrivial solution, where r is a real-valued continuous function on [c, d], then integral(d)(c) vertical bar r(t)vertical bar dt > alpha(alpha)/(alpha - 1)(alpha-1) (d - c)(a-1). (1) Moreover, a Lyapunov type inequality of the form integral(d)(c)vertical bar r(t)vertical bar dt > 3 alpha - 1/(d - c)(2 alpha-1) (3 alpha - 1/2 alpha - 1)(2 alpha-1/a), 1/2 < alpha <= 1, (2) is obtained for a sequential conformable BVP. Some examples are given and an application to conformable Sturm-Liouville eigenvalue problem is analyzed.
A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems
(Springer International Publishing, 2016) Abdeljawad, Thabet; Alzabut, Jehad; Baleanu, Dumitru
In this paper, we state and prove a new discrete q-fractional version of the Gronwall inequality. Based on this result, a particular version expressed by means of the q-Mittag-Leffler function is provided. To apply the proposed results, we prove the uniqueness and obtain an estimate for the solutions of nonlinear delay Caputo q-fractional difference system. We examine our results by providing a numerical example.
A generalized q-mittag-leffler function by q-captuo fractional linear equations
(Hindawi Publishing Corporation, 2012) Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru
Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler function is thought as the q-analogue of the one introduced previously by Kilbas and Saigo
A geometric approach for solving the density-dependent diffusion Nagumo equation
(Springer International Publishing, 2016) Baleanu, Dumitru; Darvishi, Elham; Baleanu, Dumitru
In this paper, some solutions of the density-dependent diffusion Nagumo equation are obtained by using a new approach, the Lie symmetry group-preserving scheme (LSGPS). The effects of various model parameters on the solution are investigated graphically using LSGPS. Finally, a different reduction method of PDEs is applied to construct two new analytical solutions and a first integral of the Nagumo equation.
A Gregus type common fixed point theorem of set-valued mappings in cone metric spaces
(Eudoxus Press, 2011) Abdeljawad, Thabet; Taş, Kenan; Taş, Kenan; 4971
The main purpose of this paper is to obtain a common fixed point theorem for a pair of set-valued mappings of Gregus type condition in cone metric spaces, so that the main result obtained in [13] will be generalized to cone metric spaces. The cone under consideration will be normal with normal constant K = 1
A halanay-type inequality on time scales in higher dimensional spaces
(Element, 2014) Mert, Raziye; Erbe, Lynn; Mert, Raziye; 19485
In this paper, we investigate a certain class of Halanay-type inequalities on time scales in higher dimensional spaces. By means of the obtained inequality, we derive some new global stability conditions for linear delay dynamic systems on time scales. An example is given to illustrate the results.
A Jacobi Gauss-Lobatto and Gauss-Radau collocation algorithm for solving fractional Fokker-Planck equations
(Springer, 2015) Baleanu, Dumitru; Ezz-Eldien, Samer S.; Bhrawy, Ali H.; Ahmed, Engy A.; Baleanu, Dumitru
In this article, we construct a new numerical approach for solving the time-fractional Fokker-Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss-Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss-Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker-Planck equation and the time-space-fractional Fokker-Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm
A Kamenev-type oscillation result for a linear (1+alpha)-order fractional differential equation
(Elsevier Science Inc., 2015) Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, Donal
We investigate the eventual sign changing for the solutions of the linear equation (x((alpha)))' + q(t)x = t >= 0, when the functional coefficient q satisfies the Kamenev-type restriction lim sup 1/t epsilon integral(t)(to) (t - s)epsilon q(s)ds = +infinity for some epsilon > 2; t(0) > 0. The operator x((alpha)) is the Caputo differential operator and alpha is an element of (0, 1)
A lie group approach to solve the fractional poisson equation
(Editura Academiei Romane, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Parto-Haghighi, M.
In the present paper, approximate solutions of fractional Poisson equation (FPE) have been considered using an integrator in the class of Lie groups, namely, the fictitious time integration method (FTIM). Based on the FTIM, the unknown dependent variable u(x, t) is transformed into a new variable with one more dimension. We use a fictitious time tau as the additional dimension (fictitious dimension), by transformation: v(x, t, tau) := (1 + tau)(k) u(x, t), where 0 < k <= 1 is a parameter to control the rate of convergency in the FTIM. Then the group preserving scheme (GPS) is used to integrate the new fractional partial differential equations in the augmented space R2+1. The power and the validity of the method are demonstrated using two examples.
A micro magnetic stimulator
(Chiminform Data S A, 2016) Baleanu, Dumitru; De La Roca Chiapas, Jose Maria; Perez Oliva, Hueztin Aaron; Maldonado Moreles, Martin Alejandro; Alayli, Yasser; Alvarado, Jose De Jesus Bernal; Baleanu, Dumitru; Guzman Cabrera, Rafael
Transcranial magnetic stimulus is a non-invasive method for electrically stimulating the cerebral cortex applying squared pulses with certain frequency, during variable time intervals, over particular regions of the cranium. Some specific stimuli are able to depolarize neurons and produce measurable effects such that chains of these stimuli may modify the cortical excitability of both the stimulated zone and the related remote areas through functional anatomic connections. This allows an efficient tool on treating neurological and psychiatric conditions such as depression. In this work we present a novel stimulation architecture that allows localizing the magnetic field over small spatial regions such that the field amplitude is on the order of micro-Tesla, which is three orders of magnitude less than that used in the current technology. Besides localizing the stimuli, this novel architecture will help to reduce the secondary effects of the treatment due to the low field intensity.

Browse

Browsing Fen - Edebiyat Fakültesi by Department "Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü"