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Öğe Comparison of two reliable methods to solve fractional Rosenau-Hyman equation(Wiley, 2021) Senol, Mehmet; Tasbozan, Orkun; Kurt, AliIn this study, we examine the numerical solutions of the time-fractional Rosenau-Hyman equation, which is a KdV-like model. This model demonstrates the formation of patterns in liquid drops. For this purpose, two reliable methods, residual power series method (RPSM) and perturbation-iteration algorithm (PIA), are used to obtain approximate solutions of the model. The fractional derivative is taken in the Caputo sense. Obtained results are compared with each other and the exact solutions both numerically and graphically. The outcome shows that both methods are easy to implement, powerful, and reliable. So they are ready to implement for a variety of partial fractional differential equations.Öğe Multiple-solitons for generalized (2+1)-dimensional conformable Korteweg-de Vries-Kadomtsev-Petviashvili equation(Elsevier, 2022) Akinyemi, Lanre; Senol, Mehmet; Tasbozan, Orkun; Kurt, AliThis paper studied new class of integral equation called the Korteweg-de Vries-Kadomtsev-Petviashvili (KdV-KP) equation. This equation consist of the well-known fifth-order KdV equation in the context of the Kadomtsev-Petviashvili equation. The 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 solutions. The 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 equations. Furthermore, the obtained solutions have not been reported in the previous literature and might have significant impact on future research. (c) 2021 Shanghai Jiaotong University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)Öğe NEW EXACT AND NUMERICAL SOLUTIONS OF FRACTIONAL KAUP-KUPERSHMIDT EQUATION(Asia Pacific Academic, 2019) Senol, Mehmet; Tasbozan, Orkun; Kurt, Ali; Ata, AyşeIn this article, the tanh method and the residual power series method (RPSM) are used to obtain new exact and numerical solutions of the time-fractional Kaup-Kupershmidt equation using the conformable fractional derivative definition. This definition is simple, effective and reliable in the solution procedure of the fractional differential equations that have complicated solutions with classical fractional derivative definitions like Caputo and Rieman-Liouville. © 2019 Asia Pacific Journal of Mathematics.Öğe New solutions of fractional Drinfeld-Sokolov-Wilson system in shallow water waves(Pergamon-Elsevier Science Ltd, 2018) Tasbozan, Orkun; Senol, Mehmet; Kurt, Ali; Ozkan, OzanIn this paper, we present new exact solution sets of nonlinear conformable time-fractional coupled Drinfeld-Sokolov-Wilson equation which arise in shallow water flow models, when special assumptions are used to simplify the shallow water equations by means of Sine-Gordon expansion method. We also present an analytical approximate method namely perturbation-iteration algorithm (PIA) for the system. Basic definitions of fractional derivatives are described in the conformable sense. An example is given and the results are compared to exact solutions. The results show that the presented methods are powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.Öğe New Wave Solutions of Time-Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equation as A Model of Water Waves(China Ocean Press, 2019) Atilgan, Emrah; Senol, Mehmet; Kurt, Ali; Tasbozan, OrkunThe 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.Öğe Novel solitary wave solutions to the fractional new (3+1)-dimensional Mikhailov-Novikov-Wang equation(World Scientific Publ Co Pte Ltd, 2024) Gencyigit, Mehmet; Senol, Mehmet; Kurt, Ali; Tasbozan, OrkunThis paper addresses the new (3+1)-dimensional Mikhailov-Novikov-Wang (MNW) equation with arbitrary order derivative and presents novel exact solutions of it by implementing exp(-phi(xi))-expansion, modified Kudryashov, generalized (G '/G)-expansion, and modified extended tanh-function methods. This equation emphasizes significant connection between the integrability and water waves' phenomena. Employing the conformable derivative definition, a variety of soliton (bright, dark, anti-kink) solutions of the model are obtained. Therefore, it would appear that these approaches might yield noteworthy results in producing the exact solutions to the fractional differential equations in a wide range. In addition, 2D, 3D, and contour plots of the solutions are drawn for specific values to demonstrate the physical behaviors of the solutions.Öğe Numerical Solutions of Fractional Burgers' Type Equations with Conformable Derivative(Elsevier, 2019) Senol, Mehmet; Tasbozan, Orkun; Kurt, AliIn this article, we introduce the residual power series method (RPSM) for finding approximate solutions of the time-fractional Burgers type equations using the conformable fractional derivative definition. This definition is simple and effective in the solution procedure of the fractional differential equations that have complicated solutions with classical fractional derivative definitions like Caputo and Riemann-Liouville. The results indicate the proposed method gives significant and reliable solutions.Öğe Two effective approaches for solving fractional generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves(Elsevier, 2019) Kurt, Ali; Rezazadeh, Hadi; Senol, Mehmet; Neirameh, Ahmad; Tasbozan, Orkun; Eslami, Mostafa; Mirzazadeh, MohammadIn 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 model. The fractional derivative is taken in the conformable sense. Each of the obtained exact solutions were checked by substituting them into the corresponding system with the help of Maple symbolic computation package. The results indicate that both methods are easy to implement, effective and reliable. They are therefore ready to apply for various partial fractional differential equations. (C) 2018 Shanghai Jiaotong University. Published by Elsevier B.V.Öğe Two Reliable Methods for The Solution of Fractional Coupled Burgers' Equation Arising as a Model of Polydispersive Sedimentation(Walter De Gruyter Gmbh, 2019) Kurt, Ali; Senol, Mehmet; Tasbozan, Orkun; Chand, MeharIn this article, we attain new analytical solution sets for nonlinear time-fractional coupled Burgers' equations which arise in polydispersive sedimentation in shallow water waves using exp-function method. Then we apply a semi-analytical method namely perturbation-iteration algorithm (PIA) to obtain some approximate solutions. These results are compared with obtained exact solutions by tables and surface plots. The fractional derivatives are evaluated in the conformable sense. The findings reveal that both methods are very effective and dependable for solving partial fractional differential equations.
