DSpace Arşivi :: by Yazar "Bayram, Mustafa" değerine göre listeleniyor

Yazar "Bayram, Mustafa" seçeneğine göre listele

Listeleniyor 1 - 20 / 73

An algorithm for numerical solution of some nonlinear multi-dimensional parabolic partial differential equations
(ELSEVIER, RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS, 2021) Özdemir, Neslihan; Seçer, Aydın; Bayram, Mustafa
In this research paper, a numerical method, named the three-step Ultraspherical wavelet collocation method, is presented for solving some nonlinear multi-dimensional parabolic partial differential equations. The method is third-order accurate in time. In this method, the three-step Taylor method is used to get the time derivative, while the Ultraspherical wavelet collocation method is used to get the space derivatives. Ultraspherical wavelets have good properties which make useful to carry out this aim. The presented method is developed for Burgers’ equation, Fisher–Kolmogorov–Petrovsky–Piscounov (Fisher–KPP) equation, and quasilinear parabolic equation. Three illustrative numerical problems are solved to demonstrate the efficiency, simplicity, and reliability of the presented method.
An approximate solution of fractional cable equation by homotopy analysis method
(SpringerOpen, 2014-03-16) İnç, Mustafa; Cavlak, Ebru; Bayram, Mustafa
In this article, the homotopy analysis method (HAM) is applied to solve the fractional cable equation by the Riemann-Liouville fractional partial derivative. This method includes an auxiliary parameter h which provides a convenient way of adjusting and controlling the convergence region of the series solution. In this study, approximate solutions of the fractional cable equation are obtained by HAM. We also give a convergence theorem for this equation. A suitable value for the auxiliary parameter h is determined and results obtained are presented by tables and figures.
Approximates Method for Solving an Elasticity Problem of Settled of the Elastic Ground with Variable Coefficients
(Natural Sciences Publishing (NSP), 2013-07-01) Bayram, Mustafa; Yıldırım, Kenan
In this paper, we have given numerical solutions of the elasticity problem of settled on the elastic ground with variable coefficient. Firstly, we calculate the generalized successive approximation of the given boundary value problem and we transform it into Pade series form, which give an arbitrary order for solving differential e ´ quation numerically. Secondly, we apply Homotopy Perturbation Method(HPM) to given boundary value problem. Then we compare HPM and the generalized successive approximation -Pade Approximates method by means of numerical solution of given bounda ´ ry problem. Results reveal that HPM presents more effective and accurate solution for given boundary value problem.
Bright soliton of the perturbed Schrödinger–Hirota equation with cubic–quintic–septic law of self-phase modulation in the presence of spatiotemporal dispersion
(SPRINGER HEIDELBERGTIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY, 2024) Özdemir, Neslihan; Altun, Selvi; Seçer, Aydın; Özışık, Müslüm; Bayram, Mustafa
For the first time, we intend to scrutinize both the bright optical soliton solutions of the perturbed Schrödinger–Hirota equation with cubic–quintic–septic law having the spatiotemporal dispersion and the influences of the considered equation parameters on the soliton structure. The simple version of the new extended auxiliary equation method is utilized to carry out the aims. Taking the suitable complex wave transformation, the investigated equation becomes a nonlinear ordinary differential equation. Then, a system consisting of equations in polynomial structure utilizing the technique was able to produce. The bright optical solution is generated by utilizing the presented method. Finally, numerous projections of the bright soliton are indicated to explain the propagation of optical pulses in optic fibers. Furthermore, some depictions describing the effect of the model parameter were added.
Bright soliton of the third-order nonlinear Schrödinger equation with power law of self-phase modulation in the absence of chromatic dispersion
(Springer, 2024) Durmus, Selvi Altun; Ozdemir, Neslihan; Secer, Aydin; Ozisik, Muslum; Bayram, Mustafa
In this article, we are interested in two principal topics. First, the bright optical soliton solutions of the third-order (1+1)-nonlinear Schrodinger equation including power law nonlinearity with inter-modal and spatio-temporal dispersions are perused by taking advantage of the new Kudryashov method. Second, the impacts of power law nonlinearity parameters on soliton attitude are investigated for acquired bright soliton form. With the proposed technique, the bright optical soliton solution is acquired, and 3D, contour, and 2D plots are depicted. Then, the impact of power law nonlinearity parameters on the soliton attitude has been successfully demonstrated. As is clear from this perusal power law parameters have an important impact on the soliton attitude, and this impact alters based on the soliton form. As regards our investigation, this form of the equation has not been studied with the power law nonlinearity in the absence of the chromatic dispersion for nonlinear models and the proposed method has not been applied the introduced equation before. It is expected that the consequences which are acquired in this study will shed light on the studies in this field.
The Common Solution for a Generalized Equilibrium Problem, A Variational Inequality Problem and A Hierarchical Fixed Point Problem
(SpringerOpen, 2015-02-12) Karahan, İbrahim; Seçer, Aydın; Özdemir, Murat; Bayram, Mustafa
The present paper aims to deal with a new iterative method to find a common solution of a generalized equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for a sequence of nearly nonexpansive mappings. It is proved that the proposed method converges strongly to a common solution of above problems under some assumptions. The results here improve and extend some recent corresponding results by many other authors.
Convexity of Certain q Integral Operators of p Valent Functions
(Hindawi Publishing Corporation, 2014-05-12) Selvakumaran, K. A.; Purohit, Sunil Dutt; Seçer, Aydın; Bayram, Mustafa
By applying the concept (and theory) of fractional -calculus, we first define and introduce two new -integral operators for certain analytic functions defined in the unit disc . Convexity properties of these -integral operators on some classes of analytic functions defined by a linear multiplier fractional -differintegral operator are studied. Special cases of the main results are also mentioned.
Dark-Bright Optical Soliton and Conserved Vectors to the Biswas-Arshed Equation With Third-Order Dispersions in the Absence of Self-Phase Modulation
(FRONTIERS MEDIA SA, AVENUE DU TRIBUNAL FEDERAL 34, LAUSANNE, CH-1015, SWITZERLAND, 2019) Aliyu, Aliyu Ise; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Bayram, Mustafa
The form-I version of the new celebrated Biswas-Arshed equation is studied in this work with the aid of complex envelope ansatz method. The equation is considered when self-phase is absent and velocity dispersion is negligibly small. New Dark-bright optical soliton solution of the equation emerge from the integration. The acquired solution combines the features of dark and bright solitons in one expression. The solution obtained are not yet reported in the literature. Moreover, we showed that the equation possess conservation laws (Cls).
Exact optical solitons of Radhakrishnan-Kundu-Lakshmanan equation with Kerr law nonlinearity
(World Scientific Publ Co Pte Ltd, 2019) Ghanbari, Behzad; Inc, Mustafa; Yusur, Abdullahi; Bayram, Mustafa
A new generalized exponential rational function method (GERFM) is used to acquire some new optical solitons of Radhakrishnan-Kundu-Lakshmanan (RKL) equation with Kerr nonlinearity. This equation is used to model propagation of solitons through an optical fiber. The well-known exponential rational function method is also a special case of the GERFM. The results reveal that the mentioned method is efficient and simple for solving different nonlinear partial differential equations.
Exact traveling wave solutions of the whitham-broer-kaup-like equation with time-dependent coefficients
(Natural Sciences Publishing, 2019) Bayram, Mustafa
The first integral method (FIM) is employed to solve the different type solutions of Whitham-Broer-Kaup-Like (WBKL) equation with time-dependent coefficient. We have acquired different types of solutions of this equation. We have also acquired the constraint conditions for the existence of the obtained solitons according to the parameters. It is shown that the method is effective and a direct method, based on the ring theory of commutative algebra. © 2019 NSP Natural Sciences Publishing Cor.
Exact traveling wave solutions of the whitham-broer-kaup-like equation with time-dependent coefficients
(Natural Sciences Publishing, 2019) Inc, Mustafa; Bayram, Mustafa
The first integral method (FIM) is employed to solve the different type solutions of Whitham-Broer-Kaup-Like (WBKL) equation with time-dependent coefficient. We have acquired different types of solutions of this equation. We have also acquired the constraint conditions for the existence of the obtained solitons according to the parameters. It is shown that the method is effective and a direct method, based on the ring theory of commutative algebra. © 2019 NSP.
Examination of optical soliton solutions for the perturbed Schrödinger-Hirota equation with anti-cubic law in the presence of spatiotemporal dispersion
(Springer Heidelberg, 2024) Durmus, Selvi Altun; Ozdemir, Neslihan; Secer, Aydin; Ozisik, Muslum; Bayram, Mustafa
In the current paper, the perturbed Schr & ouml;dinger-Hirota equation having anti-cubic nonlinearity is analyzed with the aid of the new Kudryashov scheme. What distinguishes this article from other articles is that it not only attains multifold analytical solutions to the underresearched model but also verifies the impact of the anti-cubic law media on soliton attitude for the first time. The algorithmic rules and solution functions of the presented method have been controlled with symbolic algebraic software, and every outcome has been approved attentively. Then, the given method has been implemented on the model under consideration for the collective test objective. With the conventional norm approximation, the nonlinear partial differential structure of the model under consideration has been turned into the ordinary differential structure by performing the wave transmutation, and then the presented technique has been implemented into the ordinary differential structure of the proposed model. After this process, we have acquired a system of linear algebraic equations and their convenient solutions. Afterward, by attaining the proper solution sets, the soliton solutions of the given model, such as bright, W-shape-like, and dark soliton forms, have been arranged, and some chosen diagrammatic views have been presented.
Extraction of soliton waves from the longitudinal wave equation with local M‑truncated derivatives
(SPRINGERVAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS, 2023) Özdemir, Neslihan; Seçer, Aydın; Bayram, Mustafa
We have extracted some soliton solutions of the fractional longitudinal wave equation with the M-truncated derivative (M-LWE), which emerges in a magneto electro-elastic circular rod. To obtain new results of this model, the unifed Riccati equation expansion and new Kudryashov methods have been utilized for the frst time. The presented methods have been productively implemented to the considered model. With the help of these two methods, new soliton waves of the M-LWE have been obtained successfully. For a better understanding of the subject and analysis of the results, 3D, contour, and 2D graphs of some soliton solutions have been presented. The interesting part of our work is that both methods, named unifed Riccati equation expansion and the new Kudryashov methods have successfully been applied for the frst time to get new soliton solutions of M-LWE.
The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers' Equations with Time-Fractional Derivative
(MDPI, ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND, 2019) Özdemir, Neslihan; Seçer, Aydın; Bayram, Mustafa
In this study, Gegenbauer wavelets are used to present two numerical methods for solving the coupled system of Burgers' equations with a time-fractional derivative. In the presented methods, we combined the operational matrix of fractional integration with the Galerkin method and the collocation method to obtain a numerical solution of the coupled system of Burgers' equations with a time-fractional derivative. The properties of Gegenbauer wavelets were used to transform this system to a system of nonlinear algebraic equations in the unknown expansion coefficients. The Galerkin method and collocation method were used to find these coefficients. The main aim of this study was to indicate that the Gegenbauer wavelets-based methods is suitable and efficient for the coupled system of Burgers' equations with time-fractional derivative. The obtained results show the applicability and efficiency of the presented Gegenbaur wavelets-based methods.
The generalized successive approximation and Pade´ approximants method for solving an elasticity problem of based on the elastic ground with variable coefficients
(BISKA Bilişim Teknoloji, 2017-01-05) Bayram, Mustafa
In this study, we have applied a generalized successive numerical technique to solve the elasticity problem of based on the elastic ground with variable coefficient. In the first stage, we have calculated the generalized successive approximation of being given BVP and in the second stage we have transformed it into Pad´e series. At the end of study a test problem has been given to clarify the method.
A Hermite Polynomial Approach for Solving the SIR Model of Epidemics
(MDPIST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND, 2018) Seçer, Aydın; Özdemir, Neslihan; Bayram, Mustafa
In this paper, the problem of the spread of a non-fatal disease in a population is solved by using the Hermite collocation method. Mathematical modeling of the problem corresponds to a three-dimensional system of nonlinear ODEs. The presented scheme reduces the problem to a nonlinear algebraic equation system by expanding the approximate solutions by using Hermite polynomials with unknown coefficients. These coefficients of the Hermite polynomials are computed by using the matrix operations of derivatives together with the collocation method. Maple software is used to carry out the computations. In addition, comparison of our method with the Homotopy perturbation method (HPM) and Laplece-Adomian decomposition method (LADM) proves accuracy of solution.
Interactive Fuzzy Goal Programming Based on Taylor Series to Solve Multiobjective Nonlinear Programming Problems With Interval Type-2 Fuzzy Numbers
(IEEE-Inst Electrical Electronics Engineers Inc, 2018) Dalman, Hasan; Bayram, Mustafa
This paper presents an interactive fuzzy goal programming (FGP) approach for solving multiobjective nonlinear programming problems (MONLPP) with interval type-2 fuzzy numbers (IT2 FNs). The cost and time of the objective functions, the resources, and the requirements of each kind of resources are taken to be trapezoidal IT2 FNs. Here, the considered problem is first transformed into an equivalent crisp MONLPP, and then the transformed MONLPP is converted into an equivalent multiobjective linear programming problem. By using a procedure based on Taylor series, this problem is reduced into a single objective linear programming problem that can be easily solved by Maple 2017 optimization toolbox. Finally, the proposed solution procedure is illustrated by two numerical examples.
Interactive goal programming algorithm with Taylor series and interval type 2 fuzzy numbers
(SPRINGER HEIDELBERG, TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY, 2019) Dalman, Hasan; Bayram, Mustafa
This paper presents an interactive fuzzy goal programming (FGP) approach for solving Multiobjective Nonlinear Programming Problems (MONLPP) with interval type 2 fuzzy numbers (IT2 FNs). The cost and time of the objective functions, and the requirements of each kind of resources are taken to be trapezoidal IT2 FNs. Here, the considered fuzzy problem is first transformed into an equivalent crisp MONLPP, and then the MONLPP is converted into an equivalent multiobjective linear programming problem (MOLPP). By using an algorithm based on Taylor series, this problem is also reduced into a single objective linear programming problem (LPP) which can be easily solved by Maple 2017 optimization toolbox. Finally, the proposed solution procedure is illustrated by a numerical example.
Invariant Investigation and Exact Solutions of Some Differential Equations with Conformable Derivatives
(Amer Scientific Publishers, 2018) Aliyu, Aliyu Isa; Inc, Mustafa; Yusuf, Abdullahi; Bayram, Mustafa
In this work, the conformable Harry-Dym, conformable logarithmic-KdV and conformable Zakharov-Ito equations are studied by using the invariant subspace method (ISM). The method determines an invariant subspace and construct the exact solutions of the partial differential equations (PDEs) by reducing them to ordinary differential equations (ODEs). As a result of the calculations, polynomial and trigonometric function solutions are derived. Ultimately, for illustrating the acquired results, some numerical simulations are performed.
Invariant subspaces, exact solutions and stability analysis of nonlinear water wave equations
(ELSEVIER, RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS, 2020) Hosseini, Kamyar; İnç, Mustafa; Shafiee, Mahmoud; Ilie, Mousa; Shafaroody, A.; Yusuf, Abdelrhman; Bayram, Mustafa
The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations (NLWWEs) in oceans through the invariant subspace scheme (ISS). In this respect, the NLWWEs which describe specific nonlinear waves are converted to a number of systems of ordinary differential equations (ODEs) such that the resulting systems can be efficiently handled by computer algebra systems. As an accomplishment, the performance of the well-designed ISS in extracting a group of exact solutions is formally confirmed. In the end, the stability analysis for the NLWWE is investigated through the linear stability scheme.

Yazar "Bayram, Mustafa" seçeneğine göre listele

Sayfa Başına Sonuç

Sıralama seçenekleri