Toward a new analytical method for solving nonlinear fractional differential equations

2008 ◽  
Vol 197 (49-50) ◽  
pp. 4173-4179 ◽  
Author(s):  
Asghar Ghorbani
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Analysis of fractional duffing oscillator

2020 ◽  
Vol 66 (2 Mar-Apr) ◽  
pp. 187 ◽  
Author(s):  
S.C. Eze
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Duffing Oscillator ◽  
Laplace Method ◽  
Nonlinear Fractional Differential Equations ◽  
Non Linear ◽  
Fractional Differential

In this contribution, a simple analytical method (which is an elegant combination of a well known methods; perturbation method and Laplace method) for solving non-linear and non-homogeneous fractional differential equations is pro- posed. In particular, the proposed method was used to analysed the fractional Duffing oscillator.The technique employed in this method can be used to analyse other nonlinear fractional differential equations, and can also be extended to non- linear partial fractional differential equations.The performance of this method is reliable, effective and gives more general solution.

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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