Browsing by Author "Dusunceli, Faruk"

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Applications of He's Semi-Inverse Variational Method and Item To the Nonlinear Long-Short Wave Interaction System
(inst Advanced Science Extension, 2019) Tekiyeh, Ramin Mehdizad; Manafian, Jalil; Baskonus, Haci Mehmet; Dusunceli, Faruk
This work deals with exact soliton solutions of the nonlinear long-short wave interaction system, utilizing two analytical methods. The system of coupled long-short wave interaction equations is studied by two analytical methods, namely, the generalized tan (phi/2)-expansion method and He's semi-inverse variational method, based upon the integration tools. Moreover, in this paper, we generalize two aforementioned methods which give new soliton wave solutions. Abundant exact traveling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play an important role in engineering and physics fields. By using these methods, exact solutions including the hyperbolic function solution, traveling wave solution, soliton solution, rational function solution, and periodic wave solution of this equation have been obtained. In addition, by using Matlab, some graphical simulations were done to see the behavior of these solutions. (C) 2019 The Authors. Published by IASE.
Fractional Approach for Diffusion Equations Arising From Oil Pollution Using the Fractional Natural Decomposition Method
(Wiley, 2025) Dusunceli, Faruk; Celik, Ercan
The main goal is to use the fractional natural decomposition approach to solve diffusion equations related to oil pollution. We examine a model that depicts the evolution of chemical processes in a network that burns helium. Elegant consolidations of nature transform with Adomian decomposition method are made possible by the Caputo operator with fractional order taken into consideration and hired algorithm. We looked at the expected model in a different sequence using fraction to show the expected algorithm's proficiency. Moreover, plots for various arbitrary orders have taken use of the physical characteristics of the obtained results. The obtained findings verify that the algorithm under consideration is highly efficient, methodical, straightforward to use, and accurate in examining the characteristics of the fractional differential system connected to related fields.
New Exact Solutions For Ablowitz-Kaup-Newell-Segur Water Wave Equation
(Yildiz Technical Univ, 2019) Dusunceli, Faruk
In this study, application of the improved Bernoulli sub-equation function method to Ablowitz-Kaup-Newell-Segur water wave equation is presented. Some new solutions have been successfully created. All the obtained solutions in this study satisfy the Ablowitz-Kaup-Newell-Segur Equation. In this paper, we have done all the calculations and graphs by Wolfram Mathematica 9.
New Exact Solutions for Generalized (3+1) Shallow Water-Like (swl) Equation
(Walter de Gruyter Gmbh, 2019) Dusunceli, Faruk
In this study, we use the improved Bernoulli sub-equation function method for exact solutions to the generalized (3+1) shallow water-like (SWL) equation. Some new solutions are successfully constructed. We carried out all the computations and the graphics plot in this paper by Wolfram Mathematica.
New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model
(HINDAWI LTD, 2019) Dusunceli, Faruk
The Konopelchenko-Dubrovsky (KD) system is presented by the application of the improved Bernoulli subequation function method (IBSEFM). First, The KD system being Nonlinear partial differential equations system is transformed into nonlinear ordinary differential equation by using a wave transformation. Last, the resulting equation is successfully explored for new explicit exact solutions including singular soliton, kink, and periodic wave solutions. All the obtained solutions in this study satisfy the Konopelchenko-Dubrovsky model. Under suitable choice of the parameter values, interesting two- and three-dimensional graphs of all the obtained solutions are plotted.
Numerical solution for high-order linear complex differential equations with variable coefficients
(WILEY, 2018) Dusunceli, Faruk; Celik, Ercan
In this paper, we have obtained the numerical solutions of complex differential equations with variable coefficients by using the Legendre Polynomials and we have performed it on two test problems. Then, we applied with different technical of error analysis to the test problems. When we compared exact solutions and numerical solutions of tables and graphs, we realized that our method is reliable, practical and functional.