A non‐local problem for a time‐fractional differential equation with the Hilfer operator on metric graph
- Author
- Erkinjon Karimov (UGent) , Zarifboy Sobirov and Jonibek Khujakulov
- Organization
- Abstract
- The main task of the present research is a non‐local boundary value problem for a time‐fractional differential equation involving Hilfer fractional derivative on a metric star graph. The main goal of this work is to stud the uniqueness and the existence of solution of the formulated problem. Using by the method of separation of variables, we find a solution of the investigated problem in the form of the Fourier series. Sufficient classes of given functions, which provide the existence and uniqueness of solution of the considered problem, are defined. Uniqueness of solution is proved, by using a priori estimates for the solution.
- Keywords
- a priori estimation, fractional derivatives and integrals, Hilfer operator, method of separation of variables, metric graph, Mittag-Leffler function, non-local problem, BOUNDARY-VALUE-PROBLEMS, DIFFUSION-EQUATIONS, WAVE-EQUATION, UNIQUENESS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01JYF8776ZF6W72GX2BKKGK10B
- MLA
- Karimov, Erkinjon, et al. “A Non‐local Problem for a Time‐fractional Differential Equation with the Hilfer Operator on Metric Graph.” MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol. 47, no. 18, 2024, pp. 13562–80, doi:10.1002/mma.10207.
- APA
- Karimov, E., Sobirov, Z., & Khujakulov, J. (2024). A non‐local problem for a time‐fractional differential equation with the Hilfer operator on metric graph. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 47(18), 13562–13580. https://doi.org/10.1002/mma.10207
- Chicago author-date
- Karimov, Erkinjon, Zarifboy Sobirov, and Jonibek Khujakulov. 2024. “A Non‐local Problem for a Time‐fractional Differential Equation with the Hilfer Operator on Metric Graph.” MATHEMATICAL METHODS IN THE APPLIED SCIENCES 47 (18): 13562–80. https://doi.org/10.1002/mma.10207.
- Chicago author-date (all authors)
- Karimov, Erkinjon, Zarifboy Sobirov, and Jonibek Khujakulov. 2024. “A Non‐local Problem for a Time‐fractional Differential Equation with the Hilfer Operator on Metric Graph.” MATHEMATICAL METHODS IN THE APPLIED SCIENCES 47 (18): 13562–13580. doi:10.1002/mma.10207.
- Vancouver
- 1.Karimov E, Sobirov Z, Khujakulov J. A non‐local problem for a time‐fractional differential equation with the Hilfer operator on metric graph. MATHEMATICAL METHODS IN THE APPLIED SCIENCES. 2024;47(18):13562–80.
- IEEE
- [1]E. Karimov, Z. Sobirov, and J. Khujakulov, “A non‐local problem for a time‐fractional differential equation with the Hilfer operator on metric graph,” MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol. 47, no. 18, pp. 13562–13580, 2024.
@article{01JYF8776ZF6W72GX2BKKGK10B,
abstract = {{The main task of the present research is a non‐local boundary value problem for a time‐fractional differential equation involving Hilfer fractional derivative on a metric star graph. The main goal of this work is to stud the uniqueness and the existence of solution of the formulated problem. Using by the method of separation of variables, we find a solution of the investigated problem in the form of the Fourier series. Sufficient classes of given functions, which provide the existence and uniqueness of solution of the considered problem, are defined. Uniqueness of solution is proved, by using a priori estimates for the solution.}},
author = {{Karimov, Erkinjon and Sobirov, Zarifboy and Khujakulov, Jonibek}},
issn = {{0170-4214}},
journal = {{MATHEMATICAL METHODS IN THE APPLIED SCIENCES}},
keywords = {{a priori estimation,fractional derivatives and integrals,Hilfer operator,method of separation of variables,metric graph,Mittag-Leffler function,non-local problem,BOUNDARY-VALUE-PROBLEMS,DIFFUSION-EQUATIONS,WAVE-EQUATION,UNIQUENESS}},
language = {{eng}},
number = {{18}},
pages = {{13562--13580}},
title = {{A non‐local problem for a time‐fractional differential equation with the Hilfer operator on metric graph}},
url = {{http://doi.org/10.1002/mma.10207}},
volume = {{47}},
year = {{2024}},
}
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