Terminal value problem for the system of fractional differential equations with additional restrictions
This paper deals with the study of terminal value problem for the system of fractional differential equations with Caputo derivative. Additional conditions are imposed on the solutions of this problem in the form of a linear vector functional. Using the theory of pseudo-inverse matrices, we obtain...
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| Format: | Article |
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Vilnius Gediminas Technical University
2025-01-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://gc.vgtu.lt/index.php/MMA/article/view/20814 |
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| author | Oleksandr Boichuk Viktor Feruk |
| author_facet | Oleksandr Boichuk Viktor Feruk |
| author_sort | Oleksandr Boichuk |
| collection | DOAJ |
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This paper deals with the study of terminal value problem for the system of fractional differential equations with Caputo derivative. Additional conditions are imposed on the solutions of this problem in the form of a linear vector functional. Using the theory of pseudo-inverse matrices, we obtain the necessary and sufficient conditions for the solvability and the general form of the solution of this boundary-value problem. In the one-dimensional case, the obtained results are generalized to the case of a multi-point boundary-value problem. The issue of obtaining similar results for the terminal value problem for the system of fractional differential equations with tempered and Ψ–tempered fractional derivatives of Caputo type is considered.
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| format | Article |
| id | doaj-art-df3eec1688964a1683152b7b6ececdb4 |
| institution | Kabale University |
| issn | 1392-6292 1648-3510 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj-art-df3eec1688964a1683152b7b6ececdb42025-01-27T16:30:20ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102025-01-0130110.3846/mma.2025.20814Terminal value problem for the system of fractional differential equations with additional restrictionsOleksandr Boichuk0Viktor Feruk1Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska st. 3, 01024 Kyiv, UkraineInstitute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska st. 3, 01024 Kyiv, Ukraine This paper deals with the study of terminal value problem for the system of fractional differential equations with Caputo derivative. Additional conditions are imposed on the solutions of this problem in the form of a linear vector functional. Using the theory of pseudo-inverse matrices, we obtain the necessary and sufficient conditions for the solvability and the general form of the solution of this boundary-value problem. In the one-dimensional case, the obtained results are generalized to the case of a multi-point boundary-value problem. The issue of obtaining similar results for the terminal value problem for the system of fractional differential equations with tempered and Ψ–tempered fractional derivatives of Caputo type is considered. https://gc.vgtu.lt/index.php/MMA/article/view/20814terminal value problemfractional differential equationCaputo derivativepseudoinverse Moore-Penrose matrixFredholm integral equation |
| spellingShingle | Oleksandr Boichuk Viktor Feruk Terminal value problem for the system of fractional differential equations with additional restrictions Mathematical Modelling and Analysis terminal value problem fractional differential equation Caputo derivative pseudoinverse Moore-Penrose matrix Fredholm integral equation |
| title | Terminal value problem for the system of fractional differential equations with additional restrictions |
| title_full | Terminal value problem for the system of fractional differential equations with additional restrictions |
| title_fullStr | Terminal value problem for the system of fractional differential equations with additional restrictions |
| title_full_unstemmed | Terminal value problem for the system of fractional differential equations with additional restrictions |
| title_short | Terminal value problem for the system of fractional differential equations with additional restrictions |
| title_sort | terminal value problem for the system of fractional differential equations with additional restrictions |
| topic | terminal value problem fractional differential equation Caputo derivative pseudoinverse Moore-Penrose matrix Fredholm integral equation |
| url | https://gc.vgtu.lt/index.php/MMA/article/view/20814 |
| work_keys_str_mv | AT oleksandrboichuk terminalvalueproblemforthesystemoffractionaldifferentialequationswithadditionalrestrictions AT viktorferuk terminalvalueproblemforthesystemoffractionaldifferentialequationswithadditionalrestrictions |