On Abstract Nonlinear Integro-Dynamic Equations in Time Scale

Abdul Awal Hadi Ahmed; Bipan Hazarika

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arXiv · 2404.11616

On Abstract Nonlinear Integro-Dynamic Equations in Time Scale

Abdul Awal Hadi Ahmed·Bipan Hazarika

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Abstract

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^{\Delta}(s) &=&Ay(s)+\mathcal{F}\left(s,y(s),\int\limits_{t_0}^{s}{\mathcal{H}(s,\tau,y(\tau))}\Delta\tau\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.

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BibTeX RIS

Abdul Awal Hadi Ahmed, Bipan Hazarika. 2024-01-01. On Abstract Nonlinear Integro-Dynamic Equations in Time Scale. https://arxiv.org/abs/2404.11616

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