On Abstract Nonlinear Integro-Dynamic Equations in Time Scale
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914760259272704 |
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| author | Ahmed, Abdul Awal Hadi Hazarika, Bipan |
| author_facet | Ahmed, Abdul Awal Hadi Hazarika, Bipan |
| contents | In this paper, we investigate the existence of the asymptotically almost automorphic solution of the following type of abstract nonlinear integro-dynamic equation \begin{eqnarray*} y^Δ(s) &=&Ay(s)+\mathcal{F}\left(s,y(s),\int\limits_{t_0}^{s}{\mathcal{H}(s,τ,y(τ))}Δτ\right),~ s\in\mathbb{T}^k, y(0)&=&y_0 \end{eqnarray*} in the Banach space of continuous function on a time scale $\mathbb{T}$. We apply the Krasnoselskii fixed point theorem to show the existence of an almost automorphic solution of the above dynamic equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_11616 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Abstract Nonlinear Integro-Dynamic Equations in Time Scale Ahmed, Abdul Awal Hadi Hazarika, Bipan General Mathematics 26A24, 26A33, 26E70, 34B15, 34N05, 39A10 In this paper, we investigate the existence of the asymptotically almost automorphic solution of the following type of abstract nonlinear integro-dynamic equation \begin{eqnarray*} y^Δ(s) &=&Ay(s)+\mathcal{F}\left(s,y(s),\int\limits_{t_0}^{s}{\mathcal{H}(s,τ,y(τ))}Δτ\right),~ s\in\mathbb{T}^k, y(0)&=&y_0 \end{eqnarray*} in the Banach space of continuous function on a time scale $\mathbb{T}$. We apply the Krasnoselskii fixed point theorem to show the existence of an almost automorphic solution of the above dynamic equation. |
| title | On Abstract Nonlinear Integro-Dynamic Equations in Time Scale |
| topic | General Mathematics 26A24, 26A33, 26E70, 34B15, 34N05, 39A10 |
| url | https://arxiv.org/abs/2404.11616 |