Time-discretization method for a multi-term time fractional differential equation with delay
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916157082042368 |
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| author | Khatoon, Areefa Raheem, Abdur Afreen, Asma |
| author_facet | Khatoon, Areefa Raheem, Abdur Afreen, Asma |
| contents | This paper discusses a multi-term time-fractional delay differential equation in a real Hilbert space. An iterative scheme for a multi-term time-fractional differential equation is established using Rothe's method. The method of semi-discretization is extended to this kind of time fractional problem with delay in the case that the time delay parameter $ν>0$ satisfies $ν\leq T$, where $T$ denotes the final time. We apply the accretivity of the operator $A$ in an iterative scheme to establish the existence and regularity of strong solutions to the considered problem. Finally, an example is provided to demonstrate the abstract result. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_07823 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-discretization method for a multi-term time fractional differential equation with delay Khatoon, Areefa Raheem, Abdur Afreen, Asma Numerical Analysis Dynamical Systems 34G20, 26A33, 37M15, 47H06, 34K30 This paper discusses a multi-term time-fractional delay differential equation in a real Hilbert space. An iterative scheme for a multi-term time-fractional differential equation is established using Rothe's method. The method of semi-discretization is extended to this kind of time fractional problem with delay in the case that the time delay parameter $ν>0$ satisfies $ν\leq T$, where $T$ denotes the final time. We apply the accretivity of the operator $A$ in an iterative scheme to establish the existence and regularity of strong solutions to the considered problem. Finally, an example is provided to demonstrate the abstract result. |
| title | Time-discretization method for a multi-term time fractional differential equation with delay |
| topic | Numerical Analysis Dynamical Systems 34G20, 26A33, 37M15, 47H06, 34K30 |
| url | https://arxiv.org/abs/2403.07823 |