Analytical and numerical results of fractional differential-difference equations. (English) Zbl 1332.37066

Summary: 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.


37N30 Dynamical systems in numerical analysis
34A08 Fractional ordinary differential equations
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