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Research Papers

Numerical Computation of a Fractional Model of Differential-Difference Equation

[+] Author and Article Information
Devendra Kumar

Department of Mathematics,
JECRC University,
Jaipur, Rajasthan 303905, India
e-mail: devendra.maths@gmail.com

Jagdev Singh

Department of Mathematics,
Jagan Nath University,
Jaipur, Rajasthan 303901, India
e-mail: jagdevsinghrathore@gmail.com

Dumitru Baleanu

Department of Mathematics,
Faculty of Arts and Sciences,
Cankaya University,
Etimesgut/Ankara 06790, Turkey;
Institute of Space Sciences,
Magurele-Bucharest 077125, Romania
e-mail: dumitru@cankaya.edu.tr

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 15, 2016; final manuscript received May 28, 2016; published online July 8, 2016. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 11(6), 061004 (Jul 08, 2016) (6 pages) Paper No: CND-16-1066; doi: 10.1115/1.4033899 History: Received February 15, 2016; Revised May 28, 2016

In the present article, we apply a numerical scheme, namely, homotopy analysis Sumudu transform algorithm, to derive the analytical and numerical solutions of a nonlinear fractional differential-difference problem occurring in nanohydrodynamics, heat conduction in nanoscale, and electronic current that flows through carbon nanotubes. The homotopy analysis Sumudu transform method (HASTM) is an inventive coupling of Sumudu transform algorithm and homotopy analysis technique that makes the calculation very easy. The fractional model is also handled with the aid of Adomian decomposition method (ADM). The numerical results derived with the help of HASTM and ADM are approximately same, so this scheme may be considered an alternative and well-organized technique for attaining analytical and numerical solutions of fractional model of discontinued problems. The analytical and numerical results derived by the application of the proposed technique reveal that the scheme is very effective, accurate, flexible, easy to apply, and computationally very appropriate for such type of fractional problems arising in physics, chemistry, biology, engineering, finance, etc.

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Figures

Grahic Jump Location
Fig. 1

The comparative study between the HASTM and exact solution

Grahic Jump Location
Fig. 2

Plots of Un(n, t) versus n at t = 1 for distinct values of γ

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