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A novel technique for (2+1)-dimensional time-fractional coupled Burgers equations

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  • Veeresha, P.
  • Prakasha, D.G.

Abstract

In the present work, the numerical solutions for time-fractional coupled Burgers equations are obtained with the aid of q-homotopy analysis transform method (q-HATM). The study of coupled Burgers equations plays a vital role in a model of evolution of the scaled volume concentration or sedimentation of the two kind particles in fluid suspensions of colloids, under the effect of gravity. In this paper, the fractional derivative is considered in Caputo sense and the proposed algorithm is an elegant mixture of homotopy analysis technique with Laplace transform. The convergence analysis for the proposed algorithm is demonstrated. The obtained solutions are presented in a series form, which converges swiftly. In order to verify the proposed technique is reliable and accurate, the numerical simulations have been conducted. The results of the study divulge that, the future technique is computationally very effective and more accurate to analyse fractional nonlinear coupled Burgers differential equations.

Suggested Citation

  • Veeresha, P. & Prakasha, D.G., 2019. "A novel technique for (2+1)-dimensional time-fractional coupled Burgers equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 324-345.
    • Handle: RePEc:eee:matcom:v:166:y:2019:i:c:p:324-345
    DOI: 10.1016/j.matcom.2019.06.005
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    References listed on IDEAS

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    1. Soliman, A.A., 2009. "On the solution of two-dimensional coupled Burgers’ equations by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1146-1155.
    2. Li, Yuanlu & Liu, Fawang & Turner, Ian W. & Li, Tao, 2018. "Time-fractional diffusion equation for signal smoothing," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 108-116.
    3. Arqub, Omar Abu & Maayah, Banan, 2018. "Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana–Baleanu fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 117-124.
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