On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side
In this article we consider the questions of one-valued solvability and numerical realization of initial value problem for a nonlinear Hilfer type fractional differential equation with maxima. By the aid of uncomplicated integral transformation based on Dirichlet formula, this initial value problem...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2021-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/488 |
| _version_ | 1827395723753160704 |
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| author | T. K. Yuldashev B. J. Kadirkulov A. R. Marakhimov |
| author_facet | T. K. Yuldashev B. J. Kadirkulov A. R. Marakhimov |
| author_sort | T. K. Yuldashev |
| collection | DOAJ |
| description |
In this article we consider the questions of one-valued solvability and numerical realization of initial value problem for a nonlinear Hilfer type fractional differential equation with maxima. By the aid of uncomplicated integral transformation based on Dirichlet formula, this initial value problem is reduced to the nonlinear Volterra type fractional integral equation. The theorem of existence and uniqueness of the solution of given initial value problem in the segment under consideration is proved. For numerical realization of solution the generalized Jacobi-Galerkin method is applied. Illustrative examples are provided.
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| first_indexed | 2024-03-08T18:38:54Z |
| format | Article |
| id | doaj.art-4f76de66a0e44965928854514bca2aa0 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:54Z |
| publishDate | 2021-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-4f76de66a0e44965928854514bca2aa02023-12-29T10:19:43ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112021-09-01103310.31489/2021m3/140-155On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand SideT. K. YuldashevB. J. KadirkulovA. R. Marakhimov In this article we consider the questions of one-valued solvability and numerical realization of initial value problem for a nonlinear Hilfer type fractional differential equation with maxima. By the aid of uncomplicated integral transformation based on Dirichlet formula, this initial value problem is reduced to the nonlinear Volterra type fractional integral equation. The theorem of existence and uniqueness of the solution of given initial value problem in the segment under consideration is proved. For numerical realization of solution the generalized Jacobi-Galerkin method is applied. Illustrative examples are provided. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/488: Ordinary differential equationequation with maximaHilfer operatorone-valued solvabilitygeneralized Jacobi–Galerkin method |
| spellingShingle | T. K. Yuldashev B. J. Kadirkulov A. R. Marakhimov On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side Қарағанды университетінің хабаршысы. Математика сериясы : Ordinary differential equation equation with maxima Hilfer operator one-valued solvability generalized Jacobi–Galerkin method |
| title | On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side |
| title_full | On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side |
| title_fullStr | On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side |
| title_full_unstemmed | On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side |
| title_short | On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side |
| title_sort | on a hilfer type fractional differential equation with nonlinear right hand side |
| topic | : Ordinary differential equation equation with maxima Hilfer operator one-valued solvability generalized Jacobi–Galerkin method |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/488 |
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