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Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws

Author

Listed:
  • Musrrat Ali

    (Department of Basic Sciences, PYD, King Faisal University, Al Ahsa 31982, Saudi Arabia)

  • Hemant Gandhi

    (Amity School of Applied Science, Amity University, Haryana, India)

  • Amit Tomar

    (Amity Institute of Applied Science, Amity University, Noida, U.P., India)

  • Dimple Singh

    (Amity School of Applied Science, Amity University, Haryana, India)

Abstract

The analysis of differential equations using Lie symmetry has been proved a very robust tool. It is also a powerful technique for reducing the order and nonlinearity of differential equations. Lie symmetry of a differential equation allows a dynamic framework for the establishment of invariant solutions of initial value and boundary value problems, and for the deduction of laws of conservations. This article is aimed at applying Lie symmetry to the fractional-order coupled nonlinear complex Hirota system of partial differential equations. This system is reduced to nonlinear fractional ordinary differential equations (FODEs) by using symmetries and explicit solutions. The reduced equations are exhibited in the form of an Erdelyi–Kober fractional (E-K) operator. The series solution of the fractional-order system and its convergence is investigated. Noether’s theorem is used to devise conservation laws.

Suggested Citation

  • Musrrat Ali & Hemant Gandhi & Amit Tomar & Dimple Singh, 2023. "Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2465-:d:1156976
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    References listed on IDEAS

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    1. Srivastava, H.M. & Dubey, V.P. & Kumar, R. & Singh, J. & Kumar, D. & Baleanu, D., 2020. "An efficient computational approach for a fractional-order biological population model with carrying capacity," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Bansal, Anupma & Kara, A.H. & Biswas, Anjan & Moshokoa, Seithuti P. & Belic, Milivoj, 2018. "Optical soliton perturbation, group invariants and conservation laws of perturbed Fokas–Lenells equation," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 275-280.
    3. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
    4. Sahoo, S. & Ray, S. Saha, 2017. "Invariant analysis with conservation laws for the time fractional Drinfeld–Sokolov–Satsuma–Hirota equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 725-733.
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