Analytic solutions of the space–time conformable fractional Klein–Gordon equation in general form

In this paper, by using a direct method based on the Jacobi elliptic functions, the exact solutions of the space-time fractional symmetric regularized long wave (SRLW) equation have been obtained. The elliptic function solutions of a nonlinear ordinary differential (auxiliary) equation (dF /dξ) 2 = P F 4 (ξ)+QF 2 (ξ)+ R have also been examined. Besides, the solutions have been found in general form including rational, trigonometric and hyperbolic functions. Moreover, the complex valued solutions, periodic solutions, and soliton solutions, have also been gained. Some solutions have been illustrated by the graphics.

show abstract

“…Some of them are seen in Ref. [32][33][34][35][36]. The Jacobi elliptic function solutions of Eq.…”

Section: Solutions Of the Space-time Fractional Srlw Eqquationmentioning

confidence: 99%

Jacobi Elliptic Function Solutions of Space-Time Fractional Symmetric Regularized Long Wave Equation

Ünal¹,

Daşçıoğlu²,

Bayram³

2021

Mathematical Sciences and Applications E-Notes

View full text Add to dashboard Cite

show abstract

“…Recently, analytical and numerical solutions of the fractional Klein-Gordon equation have been studied by many authors like [1,10,13,14,30]. There have been studies where the mass term depends on the position, [4,9,28,29] and in [15,16] the fractional Laplacian was introduced.…”

Section: Introductionmentioning

confidence: 99%

Discrete Time-Dependent Wave Equations II. Semiclassical Fractional Klein-Gordon Equation

Dasgupta¹,

Ruzhansky²,

Tushir³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The analytic method for this equation is not yet available in the literature. On the other side, in order to gain the exact solutions of different conformable fractional partial differential equations, Jacobi elliptic functions have been utilized in pervious works 17–20 . For the suggested method, the derivative using in Equation does not need to be conformable.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of time fractional Korteweg–de Vries–Zakharov–Kuznetsov equation

Ünal

Daşçıoğlu

2021

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this study, an analytic method based on the Jacobi elliptic functions has been presented to obtain the exact solutions of time fractional Korteweg–de Vries–Zakharov–Kuznetsov (KdV–ZK) equation. This equation is reduced to a nonlinear ordinary differential equation. The elementary and elliptic function solutions of this equation are investigated. Many exact solutions containing the rational, complex, trigonometric, and hyperbolic functions are also found. Besides, some of the solutions are demonstrated by the graphics.

show abstract

Analytic solutions of the space–time conformable fractional Klein–Gordon equation in general form

Cited by 8 publications

References 29 publications

Jacobi Elliptic Function Solutions of Space-Time Fractional Symmetric Regularized Long Wave Equation

Jacobi Elliptic Function Solutions of Space-Time Fractional Symmetric Regularized Long Wave Equation

Discrete Time-Dependent Wave Equations II. Semiclassical Fractional Klein-Gordon Equation

Exact solutions of time fractional Korteweg–de Vries–Zakharov–Kuznetsov equation

Contact Info

Product

Resources

About