Araştırma Çıktıları | TR-Dizin | WoS | Scopus | PubMed

Permanent URI for this communityhttps://hdl.handle.net/20.500.12416/8602

Browse

Now showing 1 - 17 of 17

A Computationally Efficient Method For a Class of Fractional Variational and Optimal Control Problems Using Fractional Gegenbauer Functions
(Editura Academiei Romane, 2018) El-Kalaawy, Ahmed A.; Doha, Eid H.; Ezz-Eldien, Samer S.; Abdelkawy, M. A.; Hafez, R. M.; Amin, A. Z. M.; Baleanu, Dumitru; Zaky, M. A.
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 Gap in the Paper A Note On Cone Metric Fixed Point Theory and Its Equivalence [Nonlinear Anal. 72(5), (2010), 2259-2261]
(Gazi Univ, 2011) Abdeljawad, Thabet; Karapınar, Erdal
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 New Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions
(Hindawi LTD, 2014) Wang, Guotao; Liu, Sanyang; Zhang, Lihong; Baleanu, Dumitru
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.
Analysis of the model of HIV-1 infection of CD4(+) T-cell with a new approach of fractional derivative
(Springer, 2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram
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.
Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations
(Pergamon-Elsevier Science Ltd, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; Bleanu, Dumitru
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
Combined Optical Solitary Waves and Conservation Laws For Nonlinear Chen-Lee-Liu Equation in Optical Fibers
(Elsevier GMBH, Urban & Fischer Verlag, 2018) İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru
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.
Comparative Study for Optimal Control Nonlinear Variable-Order Fractional Tumor Model
(Elsevier LTD., 2020) Sweilam, N. H.; Al-Mekhlafi, S. M.; Alshomrani, Ali Saleh; Baleanu, Dumitru
Discrete fractional watermark technique
(Zhejiang Univ, 2020) Wang, Zai-rong; Shiri, Babak; Baleanu, Dumitru
The fractional logistic map holds rich dynamics and is adopted to generate chaotic series. A watermark image is then encrypted and inserted into the original images. Since the encryption image takes the fractional order within (0, 1], it increases the key space and becomes difficult to attack. This study provides a robust watermark method in the protection of the copyright of hardware, images, and other electronic files.
Fractional differentiation and its applications (FDA08) PREFACE
(IOP Publishing LTD, 2009) Baleanu, Dumitru; Machado, J. A. Tenreiro
New numerical approximations for space-time fractional Burgers’ equations via a Legendre spectral-collocation method
(Editura ACAD Romane, 2015) Bhrawy, Ali H.; Zaky, Mahmoud A.; Baleanu, Dumitru
Burgers’ equation is a fundamental partial differential equation in fluid mechanics. This paper reports a new space-time spectral algorithm for obtaining an approximate solution for the space-time fractional Burgers’ equation (FBE) based on spectral shifted Legendre collocation (SLC) method in combination with the shifted Legendre operational matrix of fractional derivatives. The fractional derivatives are described in the Caputo sense. We propose a spectral shifted Legendre collocation method in both temporal and spatial discretizations for the space-time FBE. The main characteristic behind this approach is that it reduces such problem to that of solving a system of nonlinear algebraic equations that can then be solved using Newton’s iterative method. Numerical results with comparisons are given to confirm the reliability of the proposed method for FBE. © 2015, Editura Academiei Romane. All rights reserved.
On the non-commutative neutrix product of the distributions x(+)(lambda) and x(+)(mu)
(Springer Heidelberg, 2006) Fisher, Brian; Taş, Kenan
Let f and g be distributions and let g(n) = (g * delta(n))(x), where delta(n)(x) is a certain sequence converging to the Dirac delta function. The non-commutative neutrix product f circle g of f and g is defined to be the limit of the sequence {fg(n)}, provided its limit h exists in the sense that [GRAPHICS] for all functions p in D. It is proved that (x(+)(lambda)ln(p)x(+)) circle (x(+)(mu)ln(q)x(+)) = x(+)(lambda+mu)ln(p+q)x(+), (x(-)(lambda)ln(p)x(-)) circle (x(-)mu ln(q)x(-)) = x(-)(lambda+mu)ln(p+q)x(-), for lambda + mu < -1; lambda,mu,lambda+mu not equal -1,-2,... and p,q = 0,1,2.....
On the symmetric space sigma-model kinematics
(World Scientific Publ CO PTE LTD, 2007) Yılmaz, Nejat T.
The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws.
Optical solitons and modulation instability analysis with (3+1)-dimensional nonlinear Shrodinger equation
(Academic Press LTD- Elsevier Science LTD, 2017) İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru
This paper addresses the (3 + 1)-dimensional nonlinear Shrodinger equation (NLSE) that serves as the model to study the propagation of optical solitons through nonlinear optical fibers. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the solitary wave ansatz with Jaccobi elliptic function methods, we present the exact dark, bright and dark-bright or combined optical solitons to the model. The intensity as well as the nonlinear phase shift of the solitons are reported. The modulation instability aspects are discussed using the concept of linear stability analysis. The MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions.
Oscillation criteria for even order dynamic equations on time-scales
(Dynamic Publishers, Inc, 2011) Grace, Said R.; Agarwal, Ravi P.; Kaymakçalan, Billur; Baoguo, Jia; Erbe, Lynn; Mert, Raziye
Some new criteria for the oscillation of even order linear dynamic equations on time-scales of the form xΔn(t) + q(t)x(t) = 0 are established.
Research Article On Fractional SIRC Model with Salmonella Bacterial Infection
(Hindawi LTD, 2014) Baleanu, Dumitru; Rihan, Fathalla A.; Lakshmanan, S.; Rakkiyappan, R.
We propose a fractional order SIRC epidemic model to describe the dynamics of Salmonella bacterial infection in animal herds. The infection-free and endemic steady sates, of such model, are asymptotically stable under some conditions. The basic reproduction number R-0 is calculated, using next-generation matrix method, in terms of contact rate, recovery rate, and other parameters in the model. The numerical simulations of the fractional order SIRC model are performed by Caputo's derivative and using unconditionally stable implicit scheme. The obtained results give insight to the modelers and infectious disease specialists.
-Simultaneous chemometric determination of pyridoxine hydrochloride and isoniazid in tablets bymultivariate regression methods
(Wiley-Blackwell, 2010) Dinç, Erdal; Üstündağ, Ögür; Baleanu, Dumitru
The sole use of pyridoxine hydrochloride during treatment of tuberculosis gives rise to pyridoxine deficiency. Therefore, a combination of pyridoxine hydrochloride and isoniazid is used in pharmaceutical dosage form in tuberculosis treatment to reduce this side effect. In this study, two chemometric methods, partial least squares (PLS) and principal component regression (PCR), were applied to the simultaneous determination of pyridoxine (PYR) and isoniazid (ISO) in their tablets. A concentration training set comprising binary mixtures of PYR and ISO consisting of 20 different combinations were randomly prepared in 0.1 M HCl. Both multivariate calibration models were constructed using the relationships between the concentration data set (concentration data matrix) and absorbance data matrix in the spectral region 200-330 nm. The accuracy and the precision of the proposed chemometric methods were validated by analyzing synthetic mixtures containing the investigated drugs. The recovery results obtained by applying PCR and PLS calibrations to the artificial mixtures were found between 100.0 and 100.7%. Satisfactory results obtained by applying the PLS and PCR methods to both artificial and commercial samples were obtained. The results obtained in this manuscript strongly encourage us to use them for the quality control and the routine analysis of the marketing tablets containing PYR and ISO drugs. Copyright
Solitons and complexitons to the (2+1)-dimensional Heisenberg ferromagnetic spin chain model
(World Scientific Publ Co Pte Ltd, 2019) Aliyu, Aliyu Isa; Li, Yongjin; İnç, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.
This paper investigates the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain (HMF) model. The model describes the nonlinear spin dynamics of HMF. By adopting the modified F-Expansion and projective Riccati equation methods, we report the dark, combined dark-bright and envelope optical solitons, complexitons singular solutions of the equation along with the conditions that must be satisfied for solitons to exist. The physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of optical solitons.

Browse

Browsing Araştırma Çıktıları | TR-Dizin | WoS | Scopus | PubMed by Department "Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü"