Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Optical solitons to the (n+1)-dimensional nonlinear Schrodinger's equation with Kerr law and power law nonlinearities using two integration schemes
(2019) İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru
In this study, two integration techniques are employed to reach optical solitons to the (n + 1)-dimensional nonlinear Schrodinger's equation ((n + 1)-NLSE) with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented.
Invariant subspaces, exact solutions and classification of conservation laws for a coupled (1+1)-dimensional nonlinear Wu-Zhang equation
(2020) Aliyu, Aliyu Isa; Li, Yongjin; İnç, Mustafa; Baleanu, Dumitru
In this work, we apply the invariant subspace method to derive a set of invariant subspaces and solutions of the nonlinear Wu-Zhang equation which describes the dynamic behavior of dispersive long waves in fluid dynamics. The method gives logarithmic and polynomial solutions of the equation. Furthermore, the multipliers approach and new conservation theorem are employed to derive a set of conservation laws of the equation which are to the best of our knowledge reported for the first time in this work. The physical structure of the results is shown by figures of some special solutions in order to give us a better interpretation on the evolution of the solutions.
Calculus on fractals
(2015) Golmankhaneh, Alireza K.; Baleanu, Dumitru
In this chapter we present a framework and a calculus on fractals. The suggested equation has been solved and applied in physics and dynamics.
A note on (p, q)-analogue type of Fubini numbers and polynomials
(2020) Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru
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.p>
An Analytical Study of (2+1)-Dimensional Physical Models Embedded Entirely in Fractal Space
(Editura Academiei Romane, 2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, Ruwa
In this article, we analytically furnish the solution of (2 + 1)-dimensional fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (alpha, beta, gamma)-fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor's theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting alpha, beta, gamma -> 1, which indicates to some extent for a sequential memory.
A hybrid stochastic fractional order Coronavirus (2019-nCov) mathematical model
(2021) Sweilam, N. H.; Al-Mekhlafi, S. M.; Baleanu, Dumitru
In this paper, a new stochastic fractional Coronavirus (2019-nCov) model with modified parameters is presented. The proposed stochastic COVID-19 model describes well the real data of daily confirmed cases in Wuhan. Moreover, a novel fractional order operator is introduced, it is a linear combination of Caputo's fractional derivative and Riemann-Liouville integral. Milstein's higher order method is constructed with the new fractional order operator to study the model problem. The mean square stability of Milstein algorithm is proved. Numerical results and comparative studies are introduced.
Solitons of the (1 + 1) - and (2 + 1) -Dimensional Chiral Nonlinear Schrodinger Equations with the Jacobi Elliptical Function Method
(2023) Tala-Tebue, Eric; Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; Korkmaz, Alper
Our objective is to find new analytical solutions of the (1 + 1) - and (2 + 1) -dimensional Chiral nonlinear Schrodinger (CNLS) equations using the Jacobi elliptical function method. The CNLS equations play a significant role in the development of quantum mechanics, particularly in the field of quantum Hall effect. Soliton solutions of the considered models are obtained such as, cnoidal solutions, the hyperbolic solutions and the trigonometric solutions. The obtained analytical solutions are new in the literature. The stability conditions of these solutions are also given. The obtained stable solutions are presented graphically for some specific parameters. Moreover, the conditions of modulational instability for both models are provided. The proposed method can be useful to obtain the analytical solutions of nonlinear partial differential equations.
On the solutions of a fractional boundary value problem
(2018) Uğurlu, Ekin; Baleanu, Dumitru; Taş, Kenan
This paper is devoted to showing the existence and uniqueness of solution of a regular second-order nonlinear fractional differential equation subject to the ordinary boundary conditions. The Banach fixed point theorem is used to prove the results.
Asymptotic Integration of (1+Alpha)-Order Fractional Differential Equations
(Pergamon-Elsevier Science LTD, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.
We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0. (C) 2011 Elsevier Ltd. All rights reserved.
Solitary wave solutions to Gardner equation using improved tan(Ω(Υ)/2-expansion method
(2023) Akram, Ghazala; Sadaf, Maasoomah; Dawood, Mirfa; Abbas, Muhammad; Baleanu, Dumitru
In this study, the improved tan(Ω(Υ)/2-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, quantum field theory, solid-state physics and fluid dynamics. It is the simplest model for the description of water waves with dual power law nonlinearity. Hyperbolic, exponential, rational and trigonometric traveling wave solutions are obtained. The retrieved solutions include kink solitons, bright solitons, dark-bright solitons and periodic wave solutions. The efficacy of this method is determined by the comparison of the newly obtained results with already reported results.
Electro-Acoustic Device for Hip Dysplasia Assessment
(Chiminform Data SA, 2016) Perez Oliva, Huetzin; Cordova Fraga, Teodoro; Padilla Raygoza, Nicolas; Francisco, Jose; Gomez Aguilar,; Baleanu, Dumitru; Sosa, Modesto; Bernal, Jesus; Guzman-Cabrera, Rafael
A device for making diagnosis of dysplasia at the development fracture in newborns, assessment of osteoporosis and injuries of the skeletal system is presented. Its functioning is based on generation of acoustic resonance by sound transmitted through the bone under study. The device operates with a transmitter and an acoustic receiver coupled to the surface, just above the bone area under study. The measurements at the femoral bone in newborns indicate that the dominant frequency is around 160 Hz, which is consistent with other studies. Data comparisons with ultrasound technique suggest that this device could be an alternative for both dysplasia's studies of the hipbone and estimations of bone density.
Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme
(2022) Ranjbar, Hassan; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem
In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (alpha, beta)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters alpha, beta. Finally, numerical examples illustrate the effectiveness of the theoretical results.
Infectious Disease Dynamics within Advanced Fractional Operators
(2019) Defterli, Özlem; Arshad, Sadia; Jajarmi, Amin
About fractional quantization and fractional variational principles
(2009) Baleanu, Dumitru
in this paper, a new method of finding the fractional Euler-Lagrange equations within Caputo derivative is proposed by making use of the fractional generalization of the classical Fad di Bruno formula. The fractional Euler-Lagrange and the fractional Hamilton equations are obtained within the 1 + 1 field formalism. One illustrative example is analyzed. (C) 2008 Elsevier B.V. All rights reserved.
Calculus on Fractals
(De Gruyter, 2015) Golmankhaneh, Alireza K.; Baleanu, Dumitru
In this chapter we present a framework and a calculus on fractals. The sug-gested equation has been solved and applied in physics and dynamics.
NEW MULTI-FUNCTIONAL APPROACH for κ TH-ORDER DIFFERENTIABILITY GOVERNED by FRACTIONAL CALCULUS VIA APPROXIMATELY GENERALIZED (ψ, ?) -CONVEX FUNCTIONS in HILBERT SPACE
(2021) Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Baleanu, Dumitru; Chu, Yu-Ming
This work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized (ψ, ?)-convex and approximately ψ-quasiconvex function, with respect to Raina's function, which are elaborated in Hilbert space. To ensure the feasibility of the proposed concept and with the discussion of special cases, it is presented that these classes generate other classes of generalized (ψ, ?)-convex functions such as higher-order strongly (HOS) generalized (ψ, ?)-convex functions and HOS generalized ψ-quasiconvex function. The core of the proposed method is a newly developed Simpson's type of identity in the settings of Riemann-Liouville fractional integral operator. Based on the HOS generalized (ψ, ?)-convex function representation, we established several theorems and related novel consequences. The presented results demonstrate better performance for HOS generalized ψ-quasiconvex functions where we can generate several other novel classes for convex functions that exist in the relative literature. Accordingly, the assortment in this study aims at presenting a direction in the related fields. © 2021 The Author(s).
On a new class of fractional operators
(2017) Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, Dumitru
This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.
Convolution theorems associated with some integral operators and convolutions
(Taylor&Francis LTD, 2019) Al-Omari, Shrideh Khalaf Qasem; Baleanu, Dumitru
In this article, various convolution theorems involving certain weight functions and convolution products are derived. The convolution theorems we obtain are more general, convenient, and efficient than the complicated convolution theorem of the Hartley transform. Further results involving new variants of generalizations of Fourier and Hartley transforms are also discussed.
Analysis of the family of integral equation involving incomplete types of I and Ī-functions
(2023) Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D.L.; Purohit, Sunil Dutt
The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete (Formula presented.) -function (I (Formula presented.) F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (Formula presented.) -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.
Improved (G'/G)-expansion method for the time-fractional biological population model and Cahn-Hilliard equation
(2015) Baleanu, Dumitru; Uǧurlu, Yavuz; İnç, Mustafa; Kılıç, Bülent
In this paper, we used improved (G'/G)-expansion method to reach the solutions for some nonlinear time-fractional partial differential equations (fPDE). The fPDE is reduced to an ordinary differential equation (ODE) by means of Riemann-Liouille derivative and a basic variable transformation. Various types of functions are obtained for the time-fractional biological population model (fBPM) and Cahn-Hilliard (fCH) equation. Copyright © 2015 by ASME.

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