Explanipedia

The Novel Numerical Solutions of Conformable Fractional Navier-Stokes Equation with the Robust Method Open

Aslı Alkan, Hasan Bulut, Tolga Aktürk · 2025

In this study, new numerical solutions of the conformable fractional Navier-Stokes equation are obtained by the conformable q-Shehu homotopy analysis transform method. The fractional Navier-Stokes equation is an extension of the classical …

The novel numerical solutions of conformable fractional Cahn-Hilliard equation in the presence of advection and reaction terms via the novel hybrid method Open

Aslı Alkan, Hasan Bulut, Tolga Aktürk · 2025

In this paper, the novel numerical method is used to analyze the conformable fractional Cahn-Hilliard equation. The Cahn-Hilliard equation is a mathematical model employed as a crucial tool in mathematical physics, specifically for underst…

The Traveling Wave Solutions of Date–Jimbo–Kashiwara–Miwa Equation with Conformable Derivative Dependent on Time Parameter Open

Tolga Aktürk, Aslı Alkan, Hasan Bulut, Nesrin Güllüoğlu · 2024

In the paper, the traveling wave solutions of the conformable derivative Date–Jimbo–Kashiwara–Miwa equation were obtained by the modified exponential function method (MEFM). It has been seen that the wave solutions found are functions that…

Review of: "Analysis of the Spread of Covid-19 via Atangana-Baleanu Fractional Derivatives" Open

Tolga Aktürk · 2024

THE TRAVELING WAVE SOLUTIONS OF THE CONFORMABLE TIME-FRACTIONAL ZOOMERON EQUATION BY USING THE MODIFIED EXPONENTIAL FUNCTION METHOD Open

Aslı Alkan, Tolga Aktürk, Hasan Bulut · 2024

The present study focuses on the acquisition of traveling wave solutions associated with the conformable time-fractional Zoomeron equation through the utilization of the modified exponential function method (MEFM). The solution functions d…

Exact Solutions of the Stochastic Conformable Broer–Kaup Equations Open

Humaira Yasmin, Yusuf Pandır, Tolga Aktürk, Yusuf Gürefe · 2023

In this article, the exact solutions of the stochastic conformable Broer–Kaup equations with conformable derivatives which describe the bidirectional propagation of long waves in shallow water are obtained using the modified exponential fu…

The Modified Exponential Function Method for Beta Time Fractional Biswas-Arshed Equation Open

Yusuf Pandır, Tolga Aktürk, Yusuf Gürefe, Hussain Juya · 2023

In this study, the exact solutions of the Biswas-Arshed equation with the beta time derivative, which has an important role and physically means that it represents the pulse propagation in an optical fiber, nuclear, and particle physics, a…

On the Nonlinear Mathematical Model Representing the Coriolis Effect Open

Yusuf Gürefe, Yusuf Pandır, Tolga Aktürk · 2022

In this study, the traveling wave solutions of a nonlinear partial differential equation (NPDE) called as Geophysics Korteweg-de Vries (GpKdV) equation are obtained using the modified exponential function method (MEFM). Coriolis effect is …

Wave Solution Analysis of a Nonlinear Mathematical Model on Fluid Mechanics Open

Tolga Aktürk, Volkan ÇAKMAK · 2022

This study obtains some wave solutions of the B-type Kadomtsev Petviashvili equation by applying the modified exponential function method (MEFM). Due to the nature of the MEFM, two different cases are presented here, which we analyzed to o…

The New Wave Solutions in the Field of Superconductivity Open

Özlem Kırcı, Tolga Aktürk, Hasan Bulut · 2022

In this study, the Landau-Ginzburg-Higgs (LGH) equation which has the physically important wave solutions is considered. This equation is discussed via modified exponential function method (MEFM) to describe superconductivity. Some new sol…

The behavior of plasma and space-charge waves represented by nonlinear mathematical models Open

Tolga Aktürk, Çağlar Kubal · 2022

In this study, traveling wave solutions are obtained by applying the modified exponential function method (MEFM) to the conformable time-fractional (3+1)-dimensional Zakharov-Kuznetsov (FZK) and the conformable time-fractional Symmetric Re…

Investigation of Nonlinear Wave Solutions for Fusion and Fission Phenomenas Open

Tolga Aktürk, Volkan ÇAKMAK · 2022

In this study, wave solutions of the (3+1) dimensional Jimbo-Miwa equation and two different phenomena of the solution, fusion and fission, are obtained using the modified exponential functionmethod. In order to get more possible solutions…

Analyzing study for the 3D potential Yu–Toda–Sasa–Fukuyama equation in the two-layer liquid medium Open

Hajar F. Ismael, İsrafil Okumuş, Tolga Aktürk, Hasan Bulut, M.S. Osman · 2022

In this work, we use the (m+1/G′)-expansion method and the Adomian decomposition method to study the 3D potential Yu–Toda–Sasa–Fukuyama (3D-pYTSF) equation which has a good application in the two-layer liquid medium. For the first time, th…

Akışkanlar Mekaniğinde Doğrusal Olmayan Dalga Çözümlerinin İncelenmesi Open

Tolga Aktürk, Yusuf Gürefe · 2021

Bu çalışmada, (3 + 1) boyutlu potansiyel Yu-Toda-Sasa-Fukuyama (YTSF) denkleminin hareketli dalga çözümleri, modifiye üstel fonksiyon yöntemi (MEFM) kullanılarak elde edilmiştir. Bulunan çözüm fonksiyonları incelendiğinde trigonometrik, hi…

Simulation of Wave Solutions of a Mathematical Model Representing Communication Signals Open

Özlem Kırcı, Tolga Aktürk, Hasan Bulut · 2021

In this study, the Lonngren-wave equation is considered to be analyzed for its wave solutions. To implement this purpose the modified exponential function method is used and ultimately new hyperbolic, trigonometric and rational forms of th…

New Soliton Solutions of The Nonlinear Radhakrishnan-Kundu-Lakshmanan Equation With the Beta-Derivative Open

Yusuf Pandır, Yusuf Gürefe, Tolga Aktürk · 2021

In this article, the modified exponential function method is applied to find the exact solutions of the Radhakrishnan-Kundu-Lakshmanan equation with Atangana’s conformable beta-derivative. The definition of the conformable beta derivative …

Modified exponential function method for nonlinear mathematical models with Atangana conformable derivative Open

Tolga Aktürk · 2021

In this study, we investigate the analytical solutions of the modified Benjamin Bona Mahony and Sharma-Tosso-Olver equations, which are defined with Atangana conformable fractional derivative, using the modified exponential function method…

Investigation of Analytical Solutions of the Nonlinear Mathematical Model Representing Gas Overflowing Open

Yusuf Gürefe, Tolga Aktürk · 2021

In this study, traveling wave soliton solutions of hyperbolic and trigonometric functions are successfully obtained by using the modified exponential function method of the Buckley-Leverett equation. In addition to these, there are also ra…

Analysis of the Solutions of the Equation Modeled in the Field of Nonlinear Sciences Open

Tolga Aktürk, Mahşure Kübranur DİKİCİ · 2020

In this article, the travelling wave solutions of the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) equation are investigated using the modified exponential function method (MEFM). This method is used to find analytical travelli…

Interaction Solutions of Long and Short Waves in a Flexible Environment Open

Tolga Aktürk · 2020

In this study, the new traveling wave solutions resulting from the interaction of the long-short wave system were obtained by using the exp-function method. Two and three dimensional graphs of the obtained solutions were drawn by selecting…

Application of the modified exponential function method to Vakhnenko-Parkes equation Open

Gülnur Yel, Tolga Aktürk · 2020

In this paper, we submit some new travelling wave solutions for the Vakhnenko-Parkes equation via the modified exponential function method.The obtained solutions include hyperbolic, exponential, trigonometric function solutions.Regarding t…

Modified exponential function method for the KP-BBM equation Open

Tolga Aktürk, Gülnur Yel · 2020

In this study, the travelling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation were obtained by using modified exponential function method.This method provides the solution of nonlinear partial differential equati…

A New Approach to (3+1) Dimensional Boiti–Leon–Manna–Pempinelli Equation Open

Gülnur Yel, Tolga Aktürk · 2020

In this article, some new travelling wave solutions of the (3+1) dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation are obtained using the modified exponential function method. When the solution functions obtained are examined, it is …

Mathematics Teachers Understanding of the Concept of Radian Open

Hayal Yavuz Mumcu, Tolga Aktürk · 2019

Trigonometri, ilgili temel kavramların öğrenciler tarafından tam olarak anlaşılamamasına bağlı olarak matematikte öğrencilerin anlamakta güçlük çektiği konular arasında ilk sıralarda yer almaktadır

Investigation of solutions of the Pade-II equation by MEFM Open

Tolga Aktürk, Eda Günaydın · 2018

In this study, singular soliton, topological, nontopological and rational solutions of the Pade-II equation, which is a type of nonlinear partial differential equations, are obtained. By selecting the appropriate parameters, solutions were…

An application of the MEFM to the modified Boussinesq equation Open

Tolga Aktürk · 2018

In this paper, some travelling wave solutions of the Modified Boussinesq (MBQ) equation are obtained by using the modified expansion function method (MEFM). When the obtained solutions are commented, trigonometric functions including hyper…

Complex Acoustic Gravity Wave Behaviors to a Mathematical Model Arising in Nonlinear Mathematical Physics Open

Tolga Aktürk, Tukur Abdulkadir Sulaıman, Hacı Mehmet Başkonuş, Hasan Bulut · 2018

In this article, we utilize the powerful sine-Gordon expansion method (SGEM) in constructing some new solutions to the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation by using the Mathematica software. We successfully obtain some new tr…

On the new wave solutions to the Wu-Zhang system by expansion methods Open

Tolga Aktürk · 2018

In this article, Some solitary wave solutions to the Wu-Zhang system are obtained by using the modified expansion function method and the sine-Gordon expansion method. We get solitary wave solutions with the hyperbolic function structure…

An application of the new function method to the Zhiber–Shabat equation Open

Tolga Aktürk, Yusuf Gürefe, Yusuf Pandır · 2017

This paper applies a new approach including the trial equation based on the exponential function in order to find new traveling wave solutions to Zhiber-Shabat equation. By the using of this method, we obtain a new elliptic integral functi…

New function method to the (n+1)-dimensional nonlinear problems Open

Tolga Aktürk, Yusuf Gürefe, Hasan Bulut · 2017

In this study, a new approach that assumes and is applied to construct the traveling wave solutions of the (N + 1)-dimensional double sine-Gordon and (N + 1)-dimensional double sinh-cosh-Gordon equations. Some new elliptic integral functio…

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