scholarly journals Analytical method for nonlinear mathematical models with Atangana conformable derivative

2021 ◽  
Vol 67 (4 Jul-Aug) ◽  
pp. 040704
Author(s):  
T. Aktürk
Keyword(s):  
Exponential Function ◽  
Analytical Solutions ◽  
Function Method ◽  
Fractional Derivatives ◽  
Three Dimensional ◽  
Fractional Partial Differential Equations ◽  
Nonlinear Mathematical Models ◽  
Exponential Function Method ◽  
The Mathematical Model ◽  
Derivatives Of

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. Analytical solutions of the modified Benjamin Bona Mahony and Sharma-Tosso-Olver equations were obtained by using the modified exponential function method. Two, three-dimensional and contour graphics are used to understand the physical interpretations of the resulting analytical solutions to the mathematical model. When all these results and graphs are analzyed, it has been shown that the modified exponential function method is an effective method for obtaining analytical solutions for all other nonlinear fractional partial differential equations containing conformable fractional derivatives of Atangana.

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

2020 ◽  
Vol 5 (1) ◽  
pp. 309-316
Author(s):  
Gülnur Yel ◽  
Tolga Aktürk
Keyword(s):  
Exponential Function ◽  
Function Method ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Periodic Functions ◽  
New Approach ◽  
Wave Solutions ◽  
Exponential Function Method

AbstractIn 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 seen that functions with periodic functions are obtained. Two and three dimensional graphs of the travelling wave solutions of the BLMP equation are drawn by selecting the appropriate parameters

scholarly journals Fractional Diffusion Equations for Lattice and Continuum: Grünwald-Letnikov Differences and Derivatives Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Fractional Derivatives ◽  
Three Dimensional ◽  
Lattice Models ◽  
Fractional Diffusion ◽  
Lattice Diffusion ◽  
Diffusion Equations ◽  
Difference Operators ◽  
Fractional Diffusion Equations ◽  
Nonlocal Media ◽  
Derivatives Of

Fractional diffusion equations for three-dimensional lattice models based on fractional-order differences of the Grünwald-Letnikov type are suggested. These lattice fractional diffusion equations contain difference operators that describe long-range jumps from one lattice site to another. In continuum limit, the suggested lattice diffusion equations with noninteger order differences give the diffusion equations with the Grünwald-Letnikov fractional derivatives for continuum. We propose a consistent derivation of the fractional diffusion equation with the fractional derivatives of Grünwald-Letnikov type. The suggested lattice diffusion equations can be considered as a new microstructural basis of space-fractional diffusion in nonlocal media.

Three-Dimensional Strain-Based Model for the Severity Characterization of Dented Pipelines

2018 ◽  
Vol 1 (3) ◽  
Author(s):  
Chike Okoloekwe ◽  
Muntaseer Kainat ◽  
Doug Langer ◽  
Sherif Hassanien ◽  
J.J. Roger Cheng ◽  
...  
Keyword(s):  
Oil And Gas ◽  
Numerical Models ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Computation Time ◽  
Order Continuity ◽  
Element Analysis ◽  
The Mathematical Model ◽  
Derivatives Of

Oil and gas pipelines traverse long distances and are often subjected to mechanical forces that result in permanent distortion of its geometric cross section in the form of dents. In order to prioritize the repair of dents in pipelines, dents need to be ranked in order of severity. Numerical modeling via finite element analysis (FEA) to rank the dents based on the accumulated localized strain is one approach that is considered to be computationally demanding. In order to reduce the computation time with minimal effect to the completeness of the strain analysis, an approach to the analytical evaluation of strains in dented pipes based on the geometry of the deformed pipe is presented in this study. This procedure employs the use of B-spline functions, which are equipped with second-order continuity to generate displacement functions, which define the surface of the dent. The strains associated with the deformation can be determined by evaluating the derivatives of the displacement functions. The proposed technique will allow pipeline operators to rapidly determine the severity of a dent with flexibility in the choice of strain measure. The strain distribution predicted using the mathematical model proposed is benchmarked against the strains predicted by nonlinear FEA. A good correlation is observed in the strain contours predicted by the analytical and numerical models in terms of magnitude and location. A direct implication of the observed agreement is the possibility of performing concise strain analysis on dented pipes with algorithms relatively easy to implement and not as computationally demanding as FEA.

Optical soliton solutions for the nonlinear Radhakrishnan–Kundu–Lakshmanan equation

2019 ◽  
Vol 33 (32) ◽  
pp. 1950402 ◽  
Author(s):  
Behzad Ghanbari ◽  
J. F. Gómez-Aguilar
Keyword(s):  
Rational Function ◽  
Imaginary Part ◽  
Traveling Waves ◽  
Analytical Solutions ◽  
Efficient Method ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Complex Structures ◽  
Exponential Rational Function Method

In this paper, the generalized exponential rational function method is applied to obtain analytical solutions for the nonlinear Radhakrishnan–Kundu–Lakshmanan equation. We obtain novel soliton, traveling waves and kink-type solutions with complex structures. We also present the two- and three-dimensional shapes for the real and imaginary part of the solutions obtained. It is illustrated that generalized exponential rational function method (GERFM) is simple and efficient method to reach the various type of the soliton solutions.

scholarly journals New soliton properties to the ill-posed Boussinesq equation arising in nonlinear physical science

2017 ◽  
Vol 7 (3) ◽  
pp. 240-247 ◽  
Author(s):  
Serbay Duran ◽  
Muzaffer Askin ◽  
Tukur Abdulkadir Sulaiman
Keyword(s):  
Exponential Function ◽  
Physical Science ◽  
Function Method ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Nonlinear Media ◽  
Wolfram Mathematica ◽  
Ill Posed ◽  
Exponential Function Method

In manuscript, with the help of the Wolfram Mathematica 9, we employ the modified exponential function method in obtaining some new soliton solutions to the ill-posed Boussinesq equation arising in nonlinear media. Results obtained with use of technique, and also, surfaces for soliton solutions are given. We also plot the 3D and 2D of each solution obtained in this study by using the same program in the Wolfram Mathematica 9.

scholarly journals An Effective Schema for Solving Some Nonlinear Partial Differential Equation Arising In Nonlinear Physics

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Haci Mehmet Baskonus ◽  
Hasan Bulut
Keyword(s):  
Analytical Solutions ◽  
Function Method ◽  
Computational Algorithm ◽  
General Structure ◽  
Nonlinear Partial Differential Equation ◽  
Three Dimensional ◽  
Secret Key ◽  
Physical Problems ◽  
Ode Method ◽  
Physical Phenomena

AbstractIn this paper, a new computational algorithm called the "Improved Bernoulli sub-equation function method" has been proposed. This algorithm is based on the Bernoulli Sub-ODE method. Firstly, the nonlinear evaluation equations used for representing various physical phenomena are converted into ordinary differential equations by using various wave transformations. In this way, nonlinearity is preserved and represent nonlinear physical problems. The nonlinearity of physical problems together with the derivations is seen as the secret key to solve the general structure of problems.The proposed analytical schema, which is newly submitted to the literature, has been expressed comprehensively in this paper. The analytical solutions, application results, and comparisons are presented by plotting the two and three dimensional surfaces of analytical solutions obtained by using the methods proposed for some important nonlinear physical problems. Finally, a conclusion has been presented by mentioning the important discoveries in this study.

scholarly journals Exact solutions of the 2+1-dimensional Camassa–Holm Kadomtsev–Petviashvili equation

2012 ◽  
Vol 17 (3) ◽  
pp. 280-296 ◽  
Author(s):  
Ghodrat Ebadi ◽  
Nazila Yousefzadeh Fard ◽  
Houria Triki ◽  
Anjan Biswas
Keyword(s):  
Exact Solutions ◽  
Exponential Function ◽  
Soliton Solution ◽  
Function Method ◽  
Ansatz Method ◽  
Topological Soliton ◽  
Petviashvili Equation ◽  
Exponential Function Method

This paper studies the (2 + 1)-dimensional Camassa–Holm Kadomtsev–Petviashvili equation. There are a few methods that will be utilized to carry out the integration of this equation. Those are the G'/G method as well as the exponential function method. Subsequently, the ansatz method will be applied to obtain the topological soliton solution of this equation. The constraint conditions, for the existence of solitons, will also fall out of these.

scholarly journals Dark and trigonometric soliton solutions in asymmetrical Nizhnik-Novikov-Veselov equation with (2+1)-dimensional

2021 ◽  
Vol 11 (1) ◽  
pp. 92-99
Author(s):  
Haci Mehmet Baskonus
Keyword(s):  
Exponential Function ◽  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Trigonometric Function ◽  
Wolfram Mathematica ◽  
Waves Propagation ◽  
Exponential Function Method ◽  
2D And 3D

In this manuscript, new dark and trigonometric function traveling wave soliton solutions to the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation by using the modified exponential function method are successfully obtained. Along with novel dark structures, trigonometric solutions are also extracted. For deeper investigating of waves propagation on the surface, 2D and 3D graphs along with contour simulations via computational programs such as Wolfram Mathematica, Matlap softwares and so on are presented.

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