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Hyers–Ulam Stability of Order k for Euler Equation and Euler–Poisson Equation in the Calculus of Variations

Author

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  • Daniela Marian

    (Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania)

  • Sorina Anamaria Ciplea

    (Department of Management and Technology, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania)

  • Nicolaie Lungu

    (Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania)

Abstract

In this paper, we define and study Hyers–Ulam stability of order 1 for Euler’s equation and Hyers–Ulam stability of order m − 1 for the Euler–Poisson equation in the calculus of variations in two special cases, when these equations have the form y ″ ( x ) = f ( x ) and y ( m ) ( x ) = f ( x ) , respectively. We prove some estimations for J y x − J y 0 x , where y is an approximate solution and y 0 is an exact solution of the corresponding Euler and Euler-Poisson equations, respectively. We also give two examples.

Suggested Citation

  • Daniela Marian & Sorina Anamaria Ciplea & Nicolaie Lungu, 2022. "Hyers–Ulam Stability of Order k for Euler Equation and Euler–Poisson Equation in the Calculus of Variations," Mathematics, MDPI, vol. 10(15), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2556-:d:869216
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    References listed on IDEAS

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    1. Wang, Xue & Luo, Danfeng & Zhu, Quanxin, 2022. "Ulam-Hyers stability of caputo type fuzzy fractional differential equations with time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
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