Singular Cauchy Problem for a Nonlinear Fractional Differential Equation

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...

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Bibliographic Details
Main Author: Victor Orlov
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/12/22/3629
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Summary: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.
ISSN:2227-7390