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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| Format: | Article |
| Language: | English |
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MDPI AG
2024-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/22/3629 |
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| author | Victor Orlov |
| author_facet | Victor Orlov |
| author_sort | Victor Orlov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e90f1087d12543d08bb76bb33c78a858 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-e90f1087d12543d08bb76bb33c78a8582025-08-20T02:04:54ZengMDPI AGMathematics2227-73902024-11-011222362910.3390/math12223629Singular Cauchy Problem for a Nonlinear Fractional Differential EquationVictor Orlov0Institute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, Yaroslavskoye Shosse, 26, 129337 Moscow, RussiaThe 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.https://www.mdpi.com/2227-7390/12/22/3629nonlinear differential equationfractional derivativesingular pointsanalytical approximate solutiona priori estimate |
| spellingShingle | Victor Orlov Singular Cauchy Problem for a Nonlinear Fractional Differential Equation Mathematics nonlinear differential equation fractional derivative singular points analytical approximate solution a priori estimate |
| title | Singular Cauchy Problem for a Nonlinear Fractional Differential Equation |
| title_full | Singular Cauchy Problem for a Nonlinear Fractional Differential Equation |
| title_fullStr | Singular Cauchy Problem for a Nonlinear Fractional Differential Equation |
| title_full_unstemmed | Singular Cauchy Problem for a Nonlinear Fractional Differential Equation |
| title_short | Singular Cauchy Problem for a Nonlinear Fractional Differential Equation |
| title_sort | singular cauchy problem for a nonlinear fractional differential equation |
| topic | nonlinear differential equation fractional derivative singular points analytical approximate solution a priori estimate |
| url | https://www.mdpi.com/2227-7390/12/22/3629 |
| work_keys_str_mv | AT victororlov singularcauchyproblemforanonlinearfractionaldifferentialequation |