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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.17827 |
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| _version_ | 1866911280329129984 |
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| author | Epuganti, Uma Maheswara Rao Tenali, Gnana Bhaskar |
| author_facet | Epuganti, Uma Maheswara Rao Tenali, Gnana Bhaskar |
| contents | We investigate the initial value problems for non-homogeneous linear differential equations whose solutions are set-valued maps taking values in the space of nonempty compact convex subsets of $\mathbb{R}^2$, denoted by $K_{c}(\mathbb{R}^2)$. The differential formulation is based on the generalized derivative that includes the Hukuhara derivative, as well as its extensions, Bede-Gal (BG), and Plotnikov-Skripnik (PS) derivatives, and we obtain some general as well as constructive formulas for the solutions. Several illustrative examples are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17827 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-homogeneous Linear Set-Valued Differential Equations with Variable Matrix Coefficients Epuganti, Uma Maheswara Rao Tenali, Gnana Bhaskar Classical Analysis and ODEs We investigate the initial value problems for non-homogeneous linear differential equations whose solutions are set-valued maps taking values in the space of nonempty compact convex subsets of $\mathbb{R}^2$, denoted by $K_{c}(\mathbb{R}^2)$. The differential formulation is based on the generalized derivative that includes the Hukuhara derivative, as well as its extensions, Bede-Gal (BG), and Plotnikov-Skripnik (PS) derivatives, and we obtain some general as well as constructive formulas for the solutions. Several illustrative examples are provided. |
| title | Non-homogeneous Linear Set-Valued Differential Equations with Variable Matrix Coefficients |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2511.17827 |