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New Wave Solutions of Time-Fractional Coupled Boussinesq–Whitham–Broer–Kaup Equation as A Model of Water Waves

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China Ocean Engineering 2019年第4期33卷 477-483页

作者： Emrah ATILGAN mehmet senol Ali KURT Orkun TASBOZAN Department of Management Informatics Systems Mustafa Kemal University Hatay Turkey Department of Mathematics Nevsehir Haci Bektas Veli University Nevsehir Turkey Department of Mathematics Pamukkale University Denizli Turkey Department of Mathematics Mustafa Kemal University Hatay Turkey

The main purpose of this paper is to obtain the wave solutions of conformable time fractional Boussinesq–Whitham–Broer–Kaup equation arising as a model of shallow water waves. For this aim, the authors employed auxiliary equation method which is based on a nonlinear ordinary differential equation. By using conformable wave transform and chain rule, a nonlinear fractional partial differential equation is converted to a nonlinear ordinary differential equation. This is a significant impact because neither Caputo definition nor Riemann–Liouville definition satisfies the chain rule. While the exact solutions of the fractional partial derivatives cannot be obtained due to the existing drawbacks of Caputo or Riemann–Liouville definitions, the reliable solutions can be achieved for the equations defined by conformable fractional derivatives.

关键词： time fractional coupled Boussinesq–Whitham–Broer–Kaup equation conformable fractional derivative auxiliary equation method

New solutions for four novel generalized nonlinear fractional fifth-order equations

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Journal of Ocean Engineering and Science 2024年第1期9卷 59-65页

作者： mehmet senol Lanre Akinyemi Henrietta Nkansah Waleed Adel Nevsehir HacıBekta¸s Veli University Department of MathematicsNevsehirTurkey Department of Mathematics Lafayette CollegeEastonPennsylvaniaUSA Department of Mathematics University of Cape CoastCape CoastGhana Department of Mathematics and Engineering Physics Faculty of EngineeringMansoura UniversityEgypt UniversitéFrançaise dÉgypte Ismailia Desert RoadEl ShoroukCairoEgypt

In this paper,new four fifth-order fractional nonlinear equations are derived and *** frac-tional terms are defined in the conformable sense and these equations are then solved using two effective methods,namely,the sub-equation and the generalized Kudryashov *** methods were tested on the proposed models and succeeded in finding new solutions with different values of parameters.A graphical representation of some results is provided and proves the efficiency and applicability of the proposed methods for providing solutions with known physical *** methods are good candi-dates for solving other similar problems in the future.

关键词： Conformable derivative Generalized Kudryashov method Sub-equation method Riccati equation Solitons

Multiple-solitons for generalized(2+1)-dimensional conformable Korteweg-de Vries-Kadomtsev-Petviashvili equation

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Journal of Ocean Engineering and Science 2022年第6期7卷 536-542页

作者： Lanre Akinyemi mehmet senol Orkun Tasbozan Ali Kurt Department of Mathematics Lafayette CollegeEastonPennsylvaniaUSA Nevsehir HacıBektas Veli University Department of MathematicsNevsehirTurkey Mustafa Kemal University Department of MathematicsHatayTurkey Pamukkale University Department of MathematicsDenizliTurkey

This paper studied new class of integral equation called the Korteweg-de Vries-Kadomtsev-Petviashvili(KdV-KP)*** equation consist of the well-known fifth-order KdV equation in the context of the Kadomtsev-Petviashvili *** newly gathered class of sixth-order KdV-KP equation is studied using the sub-equation method to obtain several soliton-type solutions which consist of trigonometric,hyperbolic,and rational *** application of the sub-equation approach in this work draws attention to the outstanding characteristics of the suggested method and its ability to handle completely integrable ***,the obtained solutions have not been reported in the previous literature and might have significant impact on future research.

关键词： Conformable derivative Sub-equation method KdV-KP equations Multiple-soliton solutions

Analytical and approximate solutions of nonlinear Schrödinger equation with higher dimension in the anomalous dispersion regime

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Journal of Ocean Engineering and Science 2022年第2期7卷 143-154页

作者： Lanre Akinyemi mehmet senol M.S.Osman Department of Mathematics Lafayette CollegeEastonPAUSA Nev¸s ehir HacıBekta¸s Veli University Department of MathematicsNev¸s ehirTurkey Department of Mathematics Faculty of ScienceCairo UniversityGiza 12613Egypt

The generalized Riccati equation mapping method(GREMM)is used in this paper to obtain different types of soliton solutions for nonlinear Schrödinger equation with higher dimension that existed in the regimes of anomalous ***,we use the q-homotopy analysis method combined with the Laplace transform(q-HATM)to obtain approximate solutions of the bright and dark optical *** q-HATM illustrates the solutions as a rapid convergent *** addition,to show the physical behavior of the solutions obtained by the proposed techniques,the graphical representation has been provided with some parameter *** findings demonstrate that the proposed techniques are useful,efficient and reliable mathematical method for the extraction of soliton solutions.

关键词： q-homotopy analysis method Generalized Riccati equation mapping method Laplace transform

Two effective approaches for solving fractional generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves

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Journal of Ocean Engineering and Science 2019年第1期4卷 24-32页

作者： Ali Kurt Hadi Rezazadeh mehmet senol Ahmad Neirameh Orkun Tasbozan Mostafa Eslami Mohammad Mirzazadeh Department of Mathematics Mustafa Kemal UniversityHatayTurkey Faculty of Engineering Technology Amol University of Special Modern TechnologiesAmolIran Department of Mathematics Nevsehir Haci Bektas Veli UniversityNevsehirTurkey Department of Mathematics Faculty of SciencesGonbad Kavous UniversityGonbadIran Department of Mathematics Faculty of Mathematical SciencesUniversity of MazandaranBabolsarIran Department of Engineering Sciences Faculty of Technology and EngineeringEast of GuilanUniversity of GuilanRudsar-VajargahIran

In this article,two different methods,namely sub-equation method and residual power series method,have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations,which is a coupled KdV *** fractional derivative is taken in the conformable *** of the obtained exact solutions were checked by substituting them into the corresponding system with the help of Maple symbolic computation *** results indicate that both methods are easy to implement,effective and *** are therefore ready to apply for various partial fractional differential equations.

关键词： Hirota-Satsuma coupled KdV system Sub-equation method Power series method Conformable fractional derivative

A novel approach to study generalized coupled cubic Schrödinger-Korteweg-de Vries equations

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Journal of Ocean Engineering and Science 2024年第1期9卷 13-24页

作者： Lanre Akinyemi P.Veeresha M.T.Darvishi Hadi Rezazadeh mehmet senol Udoh Akpan Department of Mathematics Lafayette CollegeEastonPAUSA Department of Mathematics Christ Deemed to be UniversityBengaluru 560029India Department of Mathematics Razi UniversityKermanshah 67149Iran Faculty of Engineering Technology Amol University of Special Modern TechnologiesAmolIran Department of Mathematics Nev¸s ehir HacıBekta¸s Veli UniversityNev¸s ehirTurkey Drexel University Department of MathematicsPhiladelphiaPAUSA

The Kortewegde Vries(KdV)equation represents the propagation of long waves in dispersive media,whereas the cubic nonlinear Schrödinger(CNLS)equation depicts the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves.A model that couples these two equations seems in-triguing for simulating the interaction of long and short waves,which is important in many domains of applied sciences and engineering,and such a system has been investigated in recent *** work uses a modified Sardar sub-equation procedure to secure the soliton-type solutions of the generalized cubic nonlinear Schrödinger-Korteweg-de Vries system of *** various selections of arbitrary parameters in these solutions,the dynamic properties of some acquired solutions are represented graph-ically and *** particular,the dynamics of the bright solitons,dark solitons,mixed bright-dark solitons,W-shaped solitons,M-shaped solitons,periodic waves,and other soliton-type *** re-sults demonstrated that the proposed technique is highly efficient and effective for the aforementioned problems,as well as other nonlinear problems that may arise in the fields of mathematical physics and engineering.

关键词： CNLS equation Modiﬁed Sardar sub-equation method KdV equation Solitons Long and short waves

Robust Backstepping Control of a Quadrotor Unmanned Aerial Vehicle under Colored Noises

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Computers, Materials & Continua 2025年第1期82卷 777-798页

作者： mehmet Karahan Electrical and Electronic Engineering Department Atilim UniversityAnkara06830Turkey

Advances in software and hardware technologies have facilitated the production of quadrotor unmanned aerial vehicles(UAVs).Nowadays,people actively use quadrotor UAVs in essential missions such as search and rescue,counter-terrorism,firefighting,surveillance,and cargo *** performing these tasks,quadrotors must operate in noisy ***,a robust controller design that can control the altitude and attitude of the quadrotor in noisy environments is of great *** researchers have focused only on white Gaussian noise in their studies,whereas researchers need to consider the effects of all colored noises during the operation of the *** study aims to design a robust controller that is resistant to all colored ***,a nonlinear quadrotormodel was created with ***,a backstepping controller resistant to colored noises was *** backstepping controller was tested under Gaussian white,pink,brown,blue,and purple *** and Lyapunov-based controller designswere also carried out,and their time responses(rise time,overshoot,settling time)were compared with those of the backstepping *** the simulations,time was in seconds,altitude was in meters,and roll,pitch,and yaw references were in *** and settling time values were in seconds,and overshoot value was in *** the obtained values are examined,simulations prove that the proposed backstepping controller has the least overshoot and the shortest settling time under all noise types.

关键词： Backstepping control colored noises Gaussian noise Lyapunov stability quadrotor robustness PID control

Kefir treatment ameliorates dextran sulfate sodium-induced colitis in rats

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World Journal of Gastroenterology 2015年第46期21卷 13020-13029页

作者： Altug senol mehmet Isler Recep Sutcu Mete Akin Ebru Cakir Betul M Ceyhan M Cem Kockar Department of Gastroenterology Suleyman Demirel University School of Medicine Department of Biochemistry Suleyman Demirel University School of Medicine Department of Gastroenterology Akdeniz University School of Medicine Department of Pathology Tepecik Education and Research Hospital

AIM: To investigate the preventive effect of kefir on colitis induced with dextran sulfate sodium(DSS) in ***: Twenty-four male Wistar-albino rats were randomized into four groups: normal control,kefircontrol,colitis,and kefir-colitis groups. Rats in the normal and kefir-control groups were administered tap water as drinking water for 14 d. Rats in the colitis and kefir-colitis groups were administered a 3% DSS solution as drinking water for 8-14 d to induce colitis. Rats in the kefir-control and kefir-colitis groups were administered 5 m L kefir once a day for 14 d while rats in the normal control and colitis group were administered an identical volume of the placebo(skim milk) using an orogastric feeding tube. Clinical colitis was evaluated with reference to the disease activity index(DAI),based on daily weight loss,stool consistency,and presence of bleeding in feces. Rats were sacrificed on the 15 th day,blood specimens were collected,and colon tissues were rapidly removed. Levels of myeloperoxidase(MPO),tumor necrosisfactor(TNF)-α,interleukin(IL)-10,malondialdehyde,and inducible nitric oxide synthase(i NOS) were measured in colon ***: The DAI was lower in the kefir-colitis group than in the colitis group(on the 3rd and 5th days of colitis induction; P < 0.01). The DAI was also significantly higher in the colitis group between days 2 and 6 of colitis induction when compared to the normal control and kefir-control groups. The DAI was statistically higher only on the 6th day in the kefircolitis group when compared to that in the normal control groups. Increased colon weight and decreased colon length were observed in colitis-induced rats. Mean colon length in the colitis group was significantly shorter than that of the kefir-control group. Kefir treatment significantly decreased histologic colitis scores(P < 0.05). MPO activity in the colitis group was significantly higher than in the kefir-control group(P < 0.05). Kefir treatment significantly

关键词： Colitis Dextran sulfate sodium Inflammatory bowel

Multiple bifurcations in an early brain tumor model with piecewise constant arguments

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International Journal of Biomathematics 2018年第4期11卷 197-215页

作者： senol Kartal Department of Science and Mathematics Education Nevsehir Haci Bektas Veli University Nevsehir 50300 Turkey

In this paper, a differential equation with piecewise constant arguments modeling an early brain tumor growth is considered. The discretization process in the interval t ∈ [n, n＋1） leads to two-dimensional discrete dynamical system. By using the Schur-Cohn criterion, stability conditions of the positive equilibrium point of the system are obtained. Choosing appropriate bifurcation parameter, the existence of Neimark-Sacker and flip bifurcations is verified. In addition, the direction and stability of the Neimark-Sacker and flip bifurcations are determined by using the normal form and center manifold theory. Finally, the Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors of the system.

关键词： Piecewise constant arguments difference equation stability flip andNeimark Sacker bifurcations Lyapunov exponents.