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Symmetry analysis of initial and boundary value problems for fractional differential equations in Caputo sense

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  • Iskenderoglu, Gulistan
  • Kaya, Dogan

Abstract

In this work, we study Lie symmetry analysis of initial and boundary value problems (IBVPs) for partial differential equations (PDE) with Caputo fractional derivative. According to Bluman’s definition and theorem for the symmetry analysis of the PDE system, we determine the symmetries of the PDE with Caputo fractional derivative in general form and prove theorem for the above equation. We investigate the symmetry analysis of IBVP for a fractional diffusion and third-order fractional partial differential equation (FPDE). And as a result of applying the method, we get several solutions.

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  • Iskenderoglu, Gulistan & Kaya, Dogan, 2020. "Symmetry analysis of initial and boundary value problems for fractional differential equations in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920300862
    DOI: 10.1016/j.chaos.2020.109684
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    References listed on IDEAS

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    1. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    2. Changpin Li & Deliang Qian & YangQuan Chen, 2011. "On Riemann-Liouville and Caputo Derivatives," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, March.
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    Cited by:

    1. Kucche, Kishor D. & Sutar, Sagar T., 2021. "Analysis of nonlinear fractional differential equations involving Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Ahmed Alsaedi & Amjad F. Albideewi & Sotiris K. Ntouyas & Bashir Ahmad, 2020. "On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions," Mathematics, MDPI, vol. 8(11), pages 1-14, October.
    3. Alessandra Jannelli & Maria Paola Speciale, 2024. "Fractional Boundary Layer Flow: Lie Symmetry Analysis and Numerical Solution," Mathematics, MDPI, vol. 12(2), pages 1-10, January.
    4. Zhang, Zhi-Yong & Liu, Cheng-Bao, 2022. "Leibniz-type rule of variable-order fractional derivative and application to build Lie symmetry framework," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    5. Natalia Dilna & Michal Fečkan, 2022. "Exact Solvability Conditions for the Non-Local Initial Value Problem for Systems of Linear Fractional Functional Differential Equations," Mathematics, MDPI, vol. 10(10), pages 1-15, May.

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