Yazar "Seçer, Aydın" için listeleme
-
An algorithm for numerical solution of some nonlinear multi-dimensional parabolic partial differential equations
Özdemir, Neslihan; Seçer, Aydın; Bayram, Mustafa (ELSEVIER, RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS, 2021)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 ... -
Bright soliton of the perturbed Schrödinger–Hirota equation with cubic–quintic–septic law of self-phase modulation in the presence of spatiotemporal dispersion
Özdemir, Neslihan; Altun, Selvi; Seçer, Aydın; Özışık, Müslüm; Bayram, Mustafa (SPRINGER HEIDELBERGTIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY, 2024)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 Common Solution for a Generalized Equilibrium Problem, A Variational Inequality Problem and A Hierarchical Fixed Point Problem
Karahan, İbrahim; Seçer, Aydın; Özdemir, Murat; Bayram, Mustafa (SpringerOpen, 2015-02-12)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 ... -
Convexity of Certain q Integral Operators of p Valent Functions
Selvakumaran, K. A.; Purohit, Sunil Dutt; Seçer, Aydın; Bayram, Mustafa (Hindawi Publishing Corporation, 2014-05-12)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 ... -
Extraction of soliton waves from the longitudinal wave equation with local M‑truncated derivatives
Özdemir, Neslihan; Seçer, Aydın; Bayram, Mustafa (SPRINGERVAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS, 2023)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 Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers' Equations with Time-Fractional Derivative
Özdemir, Neslihan; Seçer, Aydın; Bayram, Mustafa (MDPI, ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND, 2019)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 ... -
A Hermite Polynomial Approach for Solving the SIR Model of Epidemics
Seçer, Aydın; Özdemir, Neslihan; Bayram, Mustafa (MDPIST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND, 2018)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 ... -
Legendre Wavelet Operational Matrix Method for Solving Fractional Differential Equations in Some Special Conditions
Seçer, Aydın; Altun, Selvi; Bayram, Mustafa (VINCA INST NUCLEAR SCI, MIHAJLA PETROVICA-ALASA 12-14 VINCA, 11037 BELGRADE. POB 522, BELGRADE, 11001, SERBIA, 2019)This paper proposes a new technique which rests upon Legendre wavelets for solving linear and non-linear forms of fractional order initial and boundary value problems. In some particular circumstances, a new operational ... -
Numerical Solution of Fractional Benney Equation
Akınlar, Mehmet Ali; Seçer, Aydın; Bayram, Mustafa (Natural Sciences Publishing (NSP), 2014-07-01)In this paper we propose a new solution technique for numerical solution of fractional Benney equation, a fourth degree nonlinear fractional partial differential equation with broad range of applications. The method could ... -
On the investigation of optical soliton solutions of cubic-quartic Fokas-Lenells and Schrodinger-Hirota equations
Özışık, Müslüm; Önder, İsmail; Esen, Handenur; Çınar, Melih; Özdemir, Neslihan; Seçer, Aydın; Bayram, Mustafa (ELSEVIER GMBH, HACKERBRUCKE 6, 80335 MUNICH, GERMANY, 2023)Purpose: When it comes to third and higher-order dispersion, the Schrödinger–Hirota equation is one of the main models developed outside the classical NLSE management models for optical soliton transmission. The cubic–quartic ... -
On the Oscillation of Fractional Order Nonlinear Differential Equations
Bayram, Mustafa; Seçer, Aydın; Adıgüzel, Hakan (Sakarya Üniversitesi, 2017-10-16)In the article, we are concerned with the oscillatory solutions of a class of fractional differential equations. By using generalized Riccati function and Hardy inequalities, we present some oscillation criterias. As a ... -
Oscillation Properties of Solutions of Fractional Difference Equations
Bayram, Mustafa; Seçer, Aydın (VINCA INST NUCLEAR SCI, MIHAJLA PETROVICA-ALASA 12-14 VINCA, 11037 BELGRADE. POB 522, BELGRADE, 11001, SERBIA, 2019)In this article, studied the properties of the oscillation of fractional difference equations, and we obtain some results. The results we obtained are an expansion and further development of highly known results. Then we ... -
Oscillatory Behavior of Solutions of Differential Equations with Fractional Order
Bayram, Mustafa; Seçer, Aydın; Adıgüzel, Hakan (Natural Sciences Publishing (NSP), 2017-05-01)In this paper, we investigated a kind of fractional differential equations with damping term. Using generalized Riccati function, we present some oscillation criteria. Finally, some examples are given to illustrative the ... -
Perturbation of dispersive optical solitons with Schrödinger–Hirota equation with Kerr law and spatio-temporal dispersion
Özdemir, Neslihan; Seçer, Aydın; Özışık, Müslüm; Bayram, Mustafa (ELSEVIER GMBH, HACKERBRUCKE 6, 80335 MUNICH, GERMANY, 2022)Objective: The principal purpose of this paper is to examine the perturbed Schrödinger–Hirota equation with the effect of spatio-temporal dispersion and Kerr law nonlinearity which governs the propagation of dispersive ... -
Revealing optical soliton solutions of Schrödinger equation having parabolic law and anti-cubic law with weakly nonlocal nonlinearity
Özdemir, Neslihan; Altun, Selvi; Seçer, Aydın; Özışık, Müslüm; Bayram, Mustafa (TAYLOR & FRANCIS LTD2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND, 2024)In this study, we purpose to ensure optical soliton solutions of the nonlinear Schrödinger equation having parabolic and anti-cubic (AC) laws with a weakly non-local nonlinearity by using the new Kudryashov method. As ... -
Sinc-Galerkin Method for Approximate Solutions of Fractional Order Boundary Value Problems
Seçer, Aydın; Alkan, Sertan; Akınlar, Mehmet Ali; Bayram, Mustafa (SpringerOpen, 2013-12-30)In this paper we present an approximate solution of a fractional order two-point boundary value problem (FBVP). We use the sinc-Galerkin method that has almost not been employed for the fractional order differential ... -
Stability, Synchronization Control and Numerical Solution of Fractional Shimizu–Morioka Dynamical System
Akınlar, Mehmet Ali; Seçer, Aydın; Bayram, Mustafa (Natural Sciences Publishing (NSP), 2014-07-01)In this paper we concern with asymptotic stability, synchronization control and numerical solution of incommensurate order fractional Shimizu–Morioka dynamical system. Firstly we prove the existence and uniqueness of the ... -
Traveling wave structures of some fourth-order nonlinear partial differential equations
Esen, Handenur; Özdemir, Neslihan; Seçer, Aydın; Bayram, Mustafa (ELSEVIER, RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS, 2023)This study presents a large family of the traveling wave solutions to the two fourth-order nonlinear partial differential equations utilizing the Riccati-Bernoulli sub-ODE method. In this method, utilizing a traveling wave ... -
Two Analytical Schemes for the Optical Soliton Solution of the (2 + 1) Hirota–Maccari System Observed in Single-Mode Fibers
Özdemir, Neslihan; Seçer, Aydın; Özışık, Müslüm; Bayram, Mustafa (MDPI, ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND, 2022)In this scientific research article, the new Kudryashov method and the tanh-coth method, which have not been applied before, are employed to construct analytical and soliton solutions of the (2 + 1)-dimensional Hirota–Maccari ... -
Wavelet-based Numerical Approaches for Solving the Korteweg-de Vries (KdV) Equation
Özdemir, Neslihan; Seçer, Aydın (Matematikçiler Derneği, 2022)In this research work, we examine the Korteweg-de Vries equation (KdV), which is utilized to formulate the propagation of water waves and occurs in different fields such as hydrodynamics waves in cold plasma acoustic ...
