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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November 2016
Research-Article
Numerical Computation of a Fractional Model of Differential-Difference Equation
Devendra Kumar,
Devendra Kumar
Department of Mathematics,
JECRC University,
Jaipur, Rajasthan 303905, India
e-mail: devendra.maths@gmail.com
JECRC University,
Jaipur, Rajasthan 303905, India
e-mail: devendra.maths@gmail.com
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Jagdev Singh,
Jagdev Singh
Department of Mathematics,
Jagan Nath University,
Jaipur, Rajasthan 303901, India
e-mail: jagdevsinghrathore@gmail.com
Jagan Nath University,
Jaipur, Rajasthan 303901, India
e-mail: jagdevsinghrathore@gmail.com
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Dumitru Baleanu
Dumitru Baleanu
Department of Mathematics,
Faculty of Arts and Sciences,
Cankaya University,
Etimesgut/Ankara 06790, Turkey;
Faculty of Arts and Sciences,
Cankaya University,
Etimesgut/Ankara 06790, Turkey;
Search for other works by this author on:
Devendra Kumar
Department of Mathematics,
JECRC University,
Jaipur, Rajasthan 303905, India
e-mail: devendra.maths@gmail.com
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
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;
Faculty of Arts and Sciences,
Cankaya University,
Etimesgut/Ankara 06790, Turkey;
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. Nov 2016, 11(6): 061004 (6 pages)
Published Online: July 8, 2016
Article history
Received:
February 15, 2016
Revised:
May 28, 2016
Citation
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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