A highly accurate numerical method for solving nonlinear time‐fractional differential difference equation

2019 ◽  
Author(s):  
Muhammad Khalid ◽  
Fareeha Sami Khan ◽  
Mariam Sultana
Keyword(s):  
Difference Equation ◽  
Numerical Method ◽  
Fractional Differential ◽  
Differential Difference Equation

Exact Solutions for Fractional Differential-Difference Equations by (G'/G)-Expansion Method with Modified Riemann-Liouville Derivative

2016 ◽  
Vol 8 (2) ◽  
pp. 293-305 ◽  
Author(s):  
Ahmet Bekir ◽  
Ozkan Guner ◽  
Burcu Ayhan ◽  
Adem C. Cevikel
Keyword(s):  
Difference Equation ◽  
Exact Solutions ◽  
Difference Equations ◽  
Applied Mathematics ◽  
Expansion Method ◽  
New Exact Solutions ◽  
Liouville Derivative ◽  
Nonlinear Lattice ◽  
Fractional Differential ◽  
Differential Difference Equation

AbstractIn this paper, the (G'/G)-expansion method is suggested to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann-Liouville derivative. The fractional complex transform is proposed to convert a fractional partial differential difference equation into its differential difference equation of integer order. With the aid of symbolic computation, we choose nonlinear lattice equations to illustrate the validity and advantages of the algorithm. It is shown that the proposed algorithm is effective and can be used for many other nonlinear lattice equations in mathematical physics and applied mathematics.

scholarly journals Analytical and numerical results of fractional differential-difference equations

2015 ◽  
Vol 7 (2) ◽  
pp. 186-199 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Fatima Riaz
Keyword(s):  
Difference Equation ◽  
Nonlinear Dynamical Systems ◽  
Linear Equations ◽  
Transformation Method ◽  
Test Problems ◽  
Nonlinear Dynamical ◽  
Fractional Differential ◽  
Differential Difference Equation ◽  
Sensitivity Approach ◽  
Infinite Linear

Abstract In this paper, we examine the fractional differential-difference equation (FDDE) by employing the proposed sensitivity approach (SA) and Adomian transformation method (ADTM). In SA the nonlinear differential-difference equation is converted to infinite linear equations which have a wide criterion to solve for the analytical solution. By ADTM, the FDDE is converted into ordinary differential-difference equation that can be solved. We test both the techniques through some test problems which are arising in nonlinear dynamical systems and found that ADTM is equivalently appropriate and simpler method to handle than SA.

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