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.
Numerical Computation of a Fractional Model of Differential-Difference Equation
Faculty of Arts and Sciences,
Etimesgut/Ankara 06790, Turkey;
Magurele-Bucharest 077125, Romania
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.
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Kumar, D., Singh, J., and Baleanu, D. (July 8, 2016). "Numerical Computation of a Fractional Model of Differential-Difference Equation." ASME. J. Comput. Nonlinear Dynam. November 2016; 11(6): 061004. https://doi.org/10.1115/1.4033899
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