On a Nonlocal Problem for Mixed-Type Equation with Partial Riemann-Liouville Fractional Derivative
The present paper presents a study on a problem with a fractional integro-differentiation operator in the boundary condition for an equation with a partial Riemann-Liouville fractional derivative. The unique solvability of the problem is proved. In the hyperbolic part of the considered domain, the f...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/2/110 |
| _version_ | 1797480097363525632 |
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| author | Menglibay Ruziev Rakhimjon Zunnunov |
| author_facet | Menglibay Ruziev Rakhimjon Zunnunov |
| author_sort | Menglibay Ruziev |
| collection | DOAJ |
| description | The present paper presents a study on a problem with a fractional integro-differentiation operator in the boundary condition for an equation with a partial Riemann-Liouville fractional derivative. The unique solvability of the problem is proved. In the hyperbolic part of the considered domain, the functional equation is solved by the iteration method. The problem is reduced to solving the Volterra integro-differential equation. |
| first_indexed | 2024-03-09T21:55:14Z |
| format | Article |
| id | doaj.art-ebbb342401fa45f4a18143c5ae714ee9 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T21:55:14Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-ebbb342401fa45f4a18143c5ae714ee92023-11-23T19:59:21ZengMDPI AGFractal and Fractional2504-31102022-02-016211010.3390/fractalfract6020110On a Nonlocal Problem for Mixed-Type Equation with Partial Riemann-Liouville Fractional DerivativeMenglibay Ruziev0Rakhimjon Zunnunov1Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, University Str. 4b, Tashkent 100174, UzbekistanInstitute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, University Str. 4b, Tashkent 100174, UzbekistanThe present paper presents a study on a problem with a fractional integro-differentiation operator in the boundary condition for an equation with a partial Riemann-Liouville fractional derivative. The unique solvability of the problem is proved. In the hyperbolic part of the considered domain, the functional equation is solved by the iteration method. The problem is reduced to solving the Volterra integro-differential equation.https://www.mdpi.com/2504-3110/6/2/110fractional order derivativeRiemann-Liouville operatorboundary value problemsingular coefficientmixed-type equation |
| spellingShingle | Menglibay Ruziev Rakhimjon Zunnunov On a Nonlocal Problem for Mixed-Type Equation with Partial Riemann-Liouville Fractional Derivative Fractal and Fractional fractional order derivative Riemann-Liouville operator boundary value problem singular coefficient mixed-type equation |
| title | On a Nonlocal Problem for Mixed-Type Equation with Partial Riemann-Liouville Fractional Derivative |
| title_full | On a Nonlocal Problem for Mixed-Type Equation with Partial Riemann-Liouville Fractional Derivative |
| title_fullStr | On a Nonlocal Problem for Mixed-Type Equation with Partial Riemann-Liouville Fractional Derivative |
| title_full_unstemmed | On a Nonlocal Problem for Mixed-Type Equation with Partial Riemann-Liouville Fractional Derivative |
| title_short | On a Nonlocal Problem for Mixed-Type Equation with Partial Riemann-Liouville Fractional Derivative |
| title_sort | on a nonlocal problem for mixed type equation with partial riemann liouville fractional derivative |
| topic | fractional order derivative Riemann-Liouville operator boundary value problem singular coefficient mixed-type equation |
| url | https://www.mdpi.com/2504-3110/6/2/110 |
| work_keys_str_mv | AT menglibayruziev onanonlocalproblemformixedtypeequationwithpartialriemannliouvillefractionalderivative AT rakhimjonzunnunov onanonlocalproblemformixedtypeequationwithpartialriemannliouvillefractionalderivative |