Matematik Bölümü Yayın Koleksiyonu

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

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Citation - WoS: 9
Citation - Scopus: 12
The Caputo-Fabrizio Time-Fractional Sharma-Tasso Equation and Its Valid Approximations
(Iop Publishing Ltd, 2022) Ilie, Mousa; Mirzazadeh, Mohammad; Baleanu, Dumitru; Park, Choonkil; Salahshour, Soheil; Hosseini, Kamyar
Studying the dynamics of solitons in nonlinear time-fractional partial differential equations has received substantial attention, in the last decades. The main aim of the current investigation is to consider the time-fractional Sharma-Tasso-Olver-Burgers (STOB) equation in the Caputo-Fabrizio (CF) context and obtain its valid approximations through adopting a mixed approach composed of the homotopy analysis method (HAM) and the Laplace transform. The existence and uniqueness of the solution of the time-fractional STOB equation in the CF context are investigated by demonstrating the Lipschitz condition for phi(x, t; u) as the kernel and giving some theorems. To illustrate the CF operator effect on the dynamics of the obtained solitons, several two- and three-dimensional plots are formally considered. It is shown that the mixed approach is capable of producing valid approximations to the time-fractional STOB equation in the CF context.
Citation - WoS: 3
Citation - Scopus: 3
Invariant Subspaces, Exact Solutions and Classification of Conservation Laws for a Coupled (1+1)-Dimensional Nonlinear Wu-Zhang Equation
(Iop Publishing Ltd, 2020) Li, Yongjin; Inc, Mustafa; Baleanu, Dumitru; Aliyu, Aliyu Isa
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.
Citation - WoS: 9
Citation - Scopus: 21
Study of Implicit Type Coupled System of Non-Integer Order Differential Equations With Antiperiodic Boundary Conditions
(Wiley, 2019) Shah, Kamal; Khan, Rahmat Ali; Baleanu, Dumitru; Samina
In this paper, the first purpose is to study existence and uniqueness of solutions to a system of implicit fractional differential equations (IFDEs) equipped with antiperiodic boundary conditions (BCs). To obtain the mentioned results, we use Schauder's and Banach fixed point theorem. The second purpose is discussing the Ulam-Hyers (UH) and generalized Ulam-Hyers (GUH) stabilities for the respective solutions. An example is provided to illustrate the established results.
About fractional calculus of singular Lagrangians
(IEEE, 2004) Baleanu, Dumitru
In this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. Despite of the complexity of solutions in the fractional case the gauge classical symmetry was preserved. Four examples of fractional singular Lagrangians were analyzed in details.
Citation - WoS: 86
Citation - Scopus: 82
On Nonautonomous Complex Wave Solutions Described by the Coupled Schrodinger-Boussinesq Equation With Variable-Coefficients
(Springer, 2018) Machado, J. A. T.; Baleanu, Dumitru; Osman, M. S.
This paper investigates the coupled Schrodinger-Boussinesq equation with variable-coefficients using the unified method. New nonautonomous complex wave solutions are obtained and classified into two categories, namely polynomial function and rational function solutions. For the polynomial functions emerge the complex solitary, complex soliton and complex elliptic wave solutions, while for the rational function are observed complex periodic rational and complex hyperbolic rational wave solutions. The physical insight and the dynamical behavior of the solutions describing the wave propagation in laser or plasma physics are discussed and analysed for different choices of the arbitrary functions in the solutions.
Citation - WoS: 7
Citation - Scopus: 9
The Investigation of Fe3o4 Atomic Aggregation in a Nanochannel in the Presence of Magnetic Field: Effects of Nanoparticles Distance Center of Mass, Temperature and Total Energy Via Molecular Dynamics Approach
(Elsevier, 2022) Fagiry, Moram A.; Sajadi, S. Mohammad; Almasri, Radwan A.; Karimipour, Arash; Li, Zhixiong; Ghaemi, Ferial; Liu, Xinglong
The computational procedure was utilized to explain the size effect of Fe3O4 nanoparticles on atomic behavior and phenomena of nanoparticles accumulation in nanochannel of ideal platinum (Pt) and the external magnetic field. Argon (Ar) atoms were considered as the base liquid, and the molecular dynamics procedure was utilized in this investigation. We utilized the Lennard-Jones potential to interact between the particles, whereas the nanochannel and nanoparticles structures were simulated. To compute the atomic manner, the quantities of nanoparticles distance center of mass, and the aggregation duration were presented. The outcomes implied that the nanoparticles size had a significant role in the accumulation. As the nanoparticles' size increased, the accumulation time of nanoparticles reached to 1.29 ns. Also, the outer magnetic field could severly postpone this event. (C) 2021 Published by Elsevier B.V.
Citation - WoS: 119
Citation - Scopus: 138
New Aspects of Fractional Biswas-Milovic Model With Mittag-Leffler Law
(Edp Sciences S A, 2019) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
This article deals with a fractional extension of Biswas-Milovic (BM) model having Kerr and parabolic law nonlinearities. The BM model plays a key role in describing the long-distance optical communications. The fractional homotopy analysis transform technique (FHATM) is applied to examine the BM equation involving Atangana-Baleanu (AB) derivative of fractional order. The FHATM is constructed by using homotopy analysis technique, Laplace transform algorithm and homotopy polynomials. The numerical simulation work is performed with the aid of maple software package. In order to demonstrate the effects of order of AB operator, variables and parameters on the displacement, the results are shown graphically. The outcomes of the present investigation are very encouraging and show that the AB fractional operator is very useful in mathematical modelling of natural phenomena.
Citation - WoS: 143
Citation - Scopus: 157
Semi-Analytical Study of Pine Wilt Disease Model With Convex Rate Under Caputo-Febrizio Fractional Order Derivative
(Pergamon-elsevier Science Ltd, 2020) Jarad, Fahd; Abdeljawad, Thabet; Shah, Kamal; Alqudah, Manar A.
In this paper, we present semi-analytical solution to Pine Wilt disease (PWD) model under the CaputoFabrizio fractional derivative (CFFD). For the proposed solution, we utilize Laplace transform coupled with Adomian decomposition method abbreviated as (LADM). The concerned method is a powerful tool to obtain semi-analytical solution for such type of nonlinear differential equations of fractional order (FODEs) involving non-singular kernel. Furthermore, we give some results for the existence of solution to the proposed model and present numerical results to verify the established analysis. (C) 2020 Elsevier Ltd. All rights reserved.
Citation - WoS: 26
Citation - Scopus: 32
On a More General Fractional Integration by Parts Formulae and Applications
(Elsevier, 2019) Gomez-Aguilar, J. F.; Jarad, Fahd; Abdeljawad, Thabet; Atangana, Abdon
The integration by part comes from the product rule of classical differentiation and integration. The concept was adapted in fractional differential and integration and has several applications in control theory. However, the formulation in fractional calculus is the classical integral of a fractional derivative of a product of a fractional derivative of a given function f and a function g. We argue that, this formulation could be done using only fractional operators: thus, we develop fractional integration by parts for fractional integrals, Riemann-Liouville, Liouville-Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. We allow the left and right fractional integrals of order alpha > 0 to act on the integrated terms instead of the usual integral and then make use of the fractional type Leibniz rules to formulate the integration by parts by means of new generalized type fractional operators with binomial coefficients defined for analytic functions. In the case alpha = 1, our formulae of fractional integration by parts results in previously obtained integration by parts in fractional calculus. The two disciplines or branches of mathematics are built differently, while classical differentiation is built with the concept of rate of change of a given function, a fractional differential operator is a convolution. (C) 2019 Elsevier B.V. All rights reserved.
Citation - WoS: 29
Citation - Scopus: 36
A Tau-Like Numerical Method for Solving Fractional Delay Integro-Differential Equations
(Elsevier, 2020) Ostadzad, M. H.; Baleanu, D.; Shahmorad, Sedaghat
In this paper, an operational matrix formulation of the Tau method is herein discussed to solve a class of delay fractional integrodifferential equations. The approximate solution is sought by using a suitable matrix representation of fractional and delay integrals. An error bound is herein for the first time discussed. Numerical examples show the effectiveness of the method. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
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.
Citation - WoS: 87
Citation - Scopus: 96
On Electromagnetic Field in Fractional Space
(Pergamon-elsevier Science Ltd, 2010) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Baleanu, Dumitru
Laplacian equation in fractional space describes complex phenomena of physics. With this view, potential of charge distribution in fractional space is derived using Gegenbauer polynomials. Multipoles and magnetic field of charges in fractional space have been obtained. (C) 2008 Elsevier Ltd. All rights reserved.
Citation - WoS: 5
Citation - Scopus: 8
Applications of the Novel Diamond Alpha Hardy-Copson Type Dynamic Inequalities To Half Linear Difference Equations
(Taylor & Francis Ltd, 2022) Kaymakcalan, Billur; Kayar, Zeynep
This paper is devoted to novel diamond alpha Hardy-Copson type dynamic inequalities, which are zeta < 0 complements of the classical ones obtained fort zeta > 1, and their applications to difference equations. We obtain two kinds of diamond alpha Hardy-Copson type inequalities for zeta < 0, one of which is mixed type and established by the convex linear combinations of the related delta and nabla inequalities while the other one is new and is obtained by using time scale calculus rather than algebra. In contrast to the works existing in the literature, these complements are derived by preserving the directions of the classical inequalities. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities obtained for zeta < 0 into one diamond alpha Hardy-Copson type inequalities and offer new types of diamond alpha Hardy-Copson type inequalities which have the same directions as the classical ones and can be considered as complementary inequalities. Moreover the application of these inequalities in the oscillation theory of half linear difference equations provides several nonoscillation criteria for such equations.
Citation - WoS: 31
Citation - Scopus: 44
Fractional Variational Principles in Action
(Iop Publishing Ltd, 2009) Baleanu, Dumitru
The fractional calculus has gained considerable importance in various fields of science and engineering, especially during the last few decades. An open issue in this emerging field is represented by the fractional variational principles area. Therefore, the fractional Euler-Lagrange and Hamilton equations started to be examined intensely during the last decade. In this paper, we review some new trends in this field and we discuss some of their potential applications.
Citation - WoS: 51
Citation - Scopus: 60
Lie Symmetry Analysis and Explicit Solutions for the Time Fractional Generalized Burgers-Huxley Equation
(Springer, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
In this work, we study the time fractional generalized Burgers-Huxley equation with Riemann-Liouville derivative via Lie symmetry analysis and power series expansion method. We transform the governing equation to nonlinear ordinary differential equation of fractional order using its Lie point symmetries. In the reduced equation, the derivative is in Erdelyi-Kober sense. We apply power series technique to derive explicit solutions for the reduced equation. The convergence of the obtained power series solutions are also derived. Some interesting Figures for the obtained solutions are presented.
From Eikonal To Antieikonal Approximations: Competition of Scales in the Framework of Schrodinger and Classical Wave Equation
(Asme, 2022) Pilar Velasco, M.; Baleanu, Dumitru; Luis Vazquez-Poletti, J.; Jimenez, Salvador; Vazquez, Luis
We present a description of certain limits associated with the Schrodinger equation, the classical wave equation, and Maxwell equations. Such limits are mainly characterized by the competition of two fundamental scales. More precisely: (1) The competition of an exploratory wavelength and the scale of fluctuations is associated with the media where the propagation takes place. From that, the universal behaviors arise eikonal and anti-eikonal. (2) In the context above, it is specially relevant and promising the study of propagation of electromagnetic waves in a media with a self-similar structure, like a fractal one. These systems offer the suggestive scenario where the eikonal and anti-eikonal behaviors are simultaneous. This kind of study requires large and massive computations that are mainly possible in the framework of the cloud computing. Recently, we started to carry out this task. (3) Finally and as a collateral aspect, we analyze the Planck constant in the interval 0 <= h <= infinity.
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.
Citation - WoS: 3
Citation - Scopus: 2
Fractional Hybrid Initial Value Problem Featuring Q-Derivatives
(Comenius Univ, 2019) Baleanu, D.; Baleanu, Dumitru; Darzi, R.; Agheli, B.; Matematik
We have perused about the existence of a solution toward hybrid initial value problem (HIVP) featuring fractional q-derivative {D-q(delta)[v(t)/h(t,v(t) max(0 <=tau <= t)vertical bar v(t)vertical bar] rho(t, v(t)), t is an element of(0,1), 0 < delta <= 1`, in which D-q(delta) denotes the Riemann-Liouville fractional q-derivative in the order of delta. In Banach algebra, by making use of a fi xed point theorem based Dhage along with mixed Lipschitz and Caratheodory condition, a way of solving the above fractional Hybrid initial value problem (FHIVP) featuring q-derivatives veri fi ed, in this study.
Citation - WoS: 2
Citation - Scopus: 2
Hamiltonian Formulation of Singular Lagrangians on Time Scales
(Iop Publishing Ltd, 2008) Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet
The Hamiltonian formulation of Lagrangian on time scale is investigated and the equivalence of Hamilton and Euler-Lagrange equations is obtained. The role of Lagrange multipliers is discussed.
Citation - WoS: 12
Citation - Scopus: 12
A Kamenev-Type Oscillation Result for a Linear (1+α)-Order Fractional Differential Equation
(Elsevier Science inc, 2015) Mustafa, Octavian G.; O'Regan, Donal; Baleanu, Dumitru
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). (C) 2015 Elsevier Inc. All rights reserved.

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