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Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems

Author

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  • Abdon Atangana
  • Emile Franc Doungmo Goufo

Abstract

We were concerned with the description of the boundary layers problems within the scope of fractional calculus. However, we will note that one of the main methods used to solve these problems is the matched asymptotic method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the matched asymptotic method to the scope of fractional derivative, we proposed a relatively new derivative called the beta-derivative . We presented some useful information for this operator. With the reward of this operator, we presented the idea of matched asymptotic method in finding solutions of the fractional boundary layers problems. The method was illustrated with an example.

Suggested Citation

  • Abdon Atangana & Emile Franc Doungmo Goufo, 2014. "Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, November.
    • Handle: RePEc:hin:jnlmpe:107535
    DOI: 10.1155/2014/107535
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    Cited by:

    1. Akram, Ghazala & Sadaf, Maasoomah & Abbas, Muhammad & Zainab, Iqra & Gillani, Syeda Rijaa, 2022. "Efficient techniques for traveling wave solutions of time-fractional Zakharov–Kuznetsov equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 607-622.
    2. Uddin, M. Hafiz & Zaman, U.H.M. & Arefin, Mohammad Asif & Akbar, M. Ali, 2022. "Nonlinear dispersive wave propagation pattern in optical fiber system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Panda, Sumati Kumari & Ravichandran, C. & Hazarika, Bipan, 2021. "Results on system of Atangana–Baleanu fractional order Willis aneurysm and nonlinear singularly perturbed boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Sahoo, Sanjay Ku & Gupta, Vikas & Dubey, Shruti, 2024. "A robust higher-order finite difference technique for a time-fractional singularly perturbed problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 43-68.
    5. Dubey, Shweta & Chakraverty, S., 2022. "Application of modified extended tanh method in solving fractional order coupled wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 509-520.

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