<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Analytical and numerical results of fractional differential-difference equations

Department of Mathematical Sciences, University of Karachi, Pakistan

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Analytical and numerical results of fractional differential-difference equations"}

In this paper, we examine the fractional differential-difference equation (FDDE) by employing the proposed sensitivity approach (SA) and Adomian transformation...

Analytical and numerical results of fractional differential-difference equations

Published Online: Feb 09, 2016

Page range: 186 - 199

Received: Mar 10, 2015

DOI: https://doi.org/10.1515/ausm-2015-0012

Keywords
differential-difference equation, transformation, sensitivity approach, numerical solutions

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Analytical and numerical results of fractional differential-difference equations

Published Online: Feb 09, 2016

Page range: 186 - 199

Received: Mar 10, 2015

DOI: https://doi.org/10.1515/ausm-2015-0012

Keywordsdifferential-difference equation, transformation, sensitivity approach, numerical solutions

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
differential-difference equation, transformation, sensitivity approach, numerical solutions