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Singular Cauchy Problem for a Nonlinear Fractional Differential Equation

Author

Listed:
  • Victor Orlov

    (Institute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, Yaroslavskoye Shosse, 26, 129337 Moscow, Russia)

Abstract

The paper studies a nonlinear equation including both fractional and ordinary derivatives. The singular Cauchy problem is considered. The theorem of the existence of uniqueness of a solution in the neighborhood of a fixed singular point of algebraic type is proved. An analytical approximate solution is built, an a priori estimate is obtained. A formula for calculating the area where the proven theorem works is obtained. The theoretical results are confirmed by a numerical experiment in both digital and graphical versions. The technology of optimizing an a priori error using an a posteriori error is demonstrated.

Suggested Citation

  • Victor Orlov, 2024. "Singular Cauchy Problem for a Nonlinear Fractional Differential Equation," Mathematics, MDPI, vol. 12(22), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3629-:d:1525494
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    References listed on IDEAS

    as
    1. Victor Orlov, 2023. "Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution," Mathematics, MDPI, vol. 11(4), pages 1-7, February.
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