Arzu Akbulut

Solving Space-Time Fractional Differential Equations by Using Modified Simple Equation Method

In this article, we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method. The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.

Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method

Abstract The auxiliary equation method presents wide applicability to handling nonlinear wave equations. In this article, we establish new exact travelling wave solutions of the nonlinear Zoomeron equation, coupled Higgs equation, and equal width wave equation. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions, and rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Throughout the article, all calculations are made with the aid of the Maple packet program.

Conservation laws and Exact Solutions of Phi-Four (Phi-4) Equation via the (G′/G, 1/G)-Expansion Method

Abstract In this article, we constructed formal Lagrangian of Phi-4 equation, and then via this formal Lagrangian, we found adjoint equation. We investigated if the Lie point symmetries of the equation satisfy invariance condition or not. Then we used conservation theorem to find conservation laws of Phi-4 equation. Finally, the exact solutions of the equation were obtained through the (G′/G, 1/G)-expansion method.

The Auto-Bäcklund transformations for the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

In this work, the homogeneous balance method is used to construct Auto-Backlund transformation of the Boiti-Leon-Manna-Pempinelli (BLMP) equation. With the aid of the transformations founded in this paper and Maple packet programme, abundant exact and explicit solutions to the BLMP equation are constructed.

Auxiliary Equation Method for Fractional Differential Equations with Modified Riemann–Liouville Derivative

Abstract: In this work, the auxiliary equation method is applied to derive exact solutions of nonlinear fractional Klein–Gordon equation and space-time fractional Symmetric Regularized Long Wave equation. Consequently, some exact solutions of these equations are successfully obtained. These solutions are formed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie’s modified Riemann–Liouville sense. The exact solutions founded by the suggested method indicate that the approach is easy to implement and powerful.

On symmetries, conservation laws and exact solutions of the nonlinear Schrödinger–Hirota equation

Abstract In this paper, conservation laws and exact solution are found for nonlinear Schrödinger–Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger–Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering.

Application of two different algorithms to the approximate long water wave equation with conformable fractional derivative

Abstract The current paper devoted on two different methods to find the exact solutions with various forms including hyperbolic, trigonometric, rational and exponential functions of fractional differential equations systems with conformable farctional derivative. We have employed the modified simple equation and exp( method here for the approximate long water wave equation. We have adopted here the fractional complex transform accompanied by properties of conformable fractional calculus for reduction of fractional partial differential equation systems to ordinary differential equation systems.

Conservation laws and exact solutions of system of Boussinesq–Burgers equations

In this work, we study conservation laws that is one of the applications of symmetries. Conservation laws has important place for differential equations and their solutions, also in all physics applications. This study deals with conservation laws of Boussinessq-Burgers equation. We used Noether approach and conservation theorem approach for finding conservation laws for this equation. Also finally, we found exact solutions of this equation by using the modified simple equation method.