Abstract
In this work, we showed a fractional derivative based iterative method for solving nonlinear time-independent equation, where the operator is affecting on a Hilbert space. We assumed that it is equally monotone and Lipschitz-continuous. We proved that the algorithm is convergent. We also have tested our method numerically previously on a fluid dynamical problem and the results showed that the algorithm is stable.
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Acknowledgements
This work was completed in the ELTE Institutional Excellence Program (1783-3/2018/FEKUTSRAT) supported by the Hungarian Ministry of Human Capacities. The project has also been supported by the European Union, co-financed by the Social Fund. EFOP-3.6.1-16-2016-0023.
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Szekeres, B.J., Izsák, F. (2019). An Iterative Method Based on Fractional Derivatives for Solving Nonlinear Equations. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_42
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DOI: https://doi.org/10.1007/978-3-030-27550-1_42
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