scholarly journals The fractional complex transformation for nonlinear fractional partial differential equations in the mathematical physics

2016 ◽  
Vol 19 (1) ◽  
pp. 59-69 ◽  
Author(s):  
Elsayed M.E. Zayed ◽  
Yasser A. Amer ◽  
Reham M.A. Shohib
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mathematical Physics ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Complex Transformation

scholarly journals On some nonlinear fractional PDEs in physics

BIBECHANA ◽  
2014 ◽  
Vol 12 ◽  
pp. 59-69
Author(s):  
Jamshad Ahmad ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Variational Iteration Method ◽  
Mathematical Physics ◽  
Inverse Transformation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Pdes ◽  
The Given ◽  
Nonlinear Nature

In this paper, we applied relatively new fractional complex transform (FCT) to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and Variational Iteration Method (VIM) is to find approximate solution of time- fractional Fornberg-Whitham and time-fractional Wu-Zhang equations. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs arising in mathematical physics and hence can be extended to other problems of diversified nonlinear nature. Numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the proposed algorithm.  DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11687BIBECHANA 12 (2015) 59-69 

scholarly journals A New Approach for Solving Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Fanwei Meng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dimensional Space ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
New Approach ◽  
New Exact Solutions ◽  
Biological Population ◽  
Complex Transformation ◽  
Dimensional Space Time

We propose a new approach for solving fractional partial differential equations based on a nonlinear fractional complex transformation and the general Riccati equation and apply it to solve the nonlinear time fractional biological population model and the (4+1)-dimensional space-time fractional Fokas equation. As a result, some new exact solutions for them are obtained. This approach can be suitable for solving fractional partial differential equations with more general forms than the method proposed by S. Zhang and H.-Q. Zhang (2011).

scholarly journals Exp-Function Method for Solving Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bin Zheng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Function Method ◽  
Space Time ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
New Exact Solutions ◽  
Complex Transformation ◽  
Liouville Derivative

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

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