scholarly journals The Soliton Solutions for Some Nonlinear Fractional Differential Equations with Beta-Derivative

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 203
Author(s):  
Erdoğan Mehmet Özkan ◽  
Ayten Özkan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Variation Method ◽  
Conformable Derivative ◽  
Ansatz Method ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential

Nonlinear fractional differential equations have gained a significant place in mathematical physics. Finding the solutions to these equations has emerged as a field of study that has attracted a lot of attention lately. In this work, He’s semi-inverse variation method and the ansatz method have been applied to find the soliton solutions for fractional Korteweg–de Vries equation, fractional equal width equation, and fractional modified equal width equation defined by Atangana’s conformable derivative (beta-derivative). These two methods are effective methods employed to get the soliton solutions of these nonlinear equations. All of the calculations in this work have been obtained using the Maple program and the solutions have been replaced in the equations and their accuracy has been confirmed. In addition, graphics of some of the solutions are also included. The found solutions in this study have the potential to be useful in mathematical physics and engineering.

scholarly journals Soliton solutions of nonlinear fractional differential equations with its applications in mathematical physics

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 422
Author(s):  
A. C. Çevikel ◽  
E. Aksoy
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Complex Transform ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Present Technique ◽  
Fractional Differential

Generalized Kudryashov method has been used to private type of nonlinear fractional differential equations. Firstly, we proposed a fractional complex transform to convert fractional differential equations into ordinary differential equations. Three applications were given to demonstrate the effectiveness of the present technique. As a result, abundant types of exact analytical solutions are obtained.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

Multiple Solutions of Nonlinear Fractional Differential Equations with p-Laplacian Operator and Nonlinear Boundary Conditions

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Yiliang Liu ◽  
Liang Lu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Upper And Lower Solutions ◽  
Nonlinear Boundary Conditions ◽  
Laplacian Operator ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential

AbstractIn this paper, we deal with multiple solutions of fractional differential equations with p-Laplacian operator and nonlinear boundary conditions. By applying the Amann theorem and the method of upper and lower solutions, we obtain some new results on the multiple solutions. An example is given to illustrate our results.

scholarly journals Existence results for coupled nonlinear fractional differential equations of different orders with nonlocal coupled boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Alsaedi ◽  
Soha Hamdan ◽  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Arbitrary Domain ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Coupled Boundary Conditions ◽  
Fractional Differential

AbstractThis paper is concerned with the solvability of coupled nonlinear fractional differential equations of different orders supplemented with nonlocal coupled boundary conditions on an arbitrary domain. The tools of the fixed point theory are applied to obtain the criteria ensuring the existence and uniqueness of solutions of the problem at hand. Examples illustrating the main results are presented.

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