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Non-perturbative analytical solutions of the space- and time-fractional Burgers equations

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  • Momani, Shaher

Abstract

Non-perturbative analytical solutions for the generalized Burgers equation with time- and space-fractional derivatives of order α and β, 0<α,β⩽1, are derived using Adomian decomposition method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed.

Suggested Citation

  • Momani, Shaher, 2006. "Non-perturbative analytical solutions of the space- and time-fractional Burgers equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 930-937.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:930-937
    DOI: 10.1016/j.chaos.2005.09.002
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    References listed on IDEAS

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    1. Kaya, Doǧan & Yokus, Asif, 2002. "A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 60(6), pages 507-512.
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    Cited by:

    1. Rashid Nawaz & Laiq Zada & Abraiz Khattak & Muhammad Jibran & Adam Khan, 2019. "Optimum Solutions of Fractional Order Zakharov–Kuznetsov Equations," Complexity, Hindawi, vol. 2019, pages 1-9, December.
    2. Yu, Yongguang & Li, Han-Xiong, 2009. "Application of the multistage homotopy-perturbation method to solve a class of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2330-2337.
    3. Rao, Anjali & Vats, Ramesh Kumar & Yadav, Sanjeev, 2024. "Numerical study of nonlinear time-fractional Caudrey–Dodd–Gibbon–Sawada–Kotera equation arising in propagation of waves," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    4. Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Qiu, Wenlin & Chen, Hongbin & Zheng, Xuan, 2019. "An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 298-314.
    6. Yadav, Swati & Pandey, Rajesh K., 2020. "Numerical approximation of fractional burgers equation with Atangana–Baleanu derivative in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    7. Memarbashi, Reza, 2008. "Numerical solution of the Laplace equation in annulus by Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 138-143.
    8. Safyan Mukhtar & Salah Abuasad & Ishak Hashim & Samsul Ariffin Abdul Karim, 2020. "Effective Method for Solving Different Types of Nonlinear Fractional Burgers’ Equations," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    9. Yu, Yongguang & Li, Han-Xiong, 2008. "The synchronization of fractional-order Rössler hyperchaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1393-1403.
    10. Odibat, Zaid M., 2009. "Computational algorithms for computing the fractional derivatives of functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2013-2020.

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