Asymptotic behavior of solutions of a time-space fractional diffusive Volterra equation

Sofwah Ahmad; Mokhtar Kirane

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arXiv · 2502.14725

Asymptotic behavior of solutions of a time-space fractional diffusive Volterra equation

Sofwah Ahmad·Mokhtar Kirane

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Abstract

In this paper, we study the time-space fractional differential equation of the Volterra type: \begin{align*} {D}^\alpha_{0 \vert t} (u) +(-\Delta_N)^{\sigma}u &= u(1+au-bu^2)-au\int_0^t {K}(t-s) u(\cdot) \, ds, \end{align*} where $a,b>0$ are given constants, $\alpha,\sigma \in (0,1)$, equipped with a homogeneous Neumann's boundary condition and a positive initial data. The boundedness and uniform continuity of the solution on the entire $\mathbb{R}^+$ are established. Moreover, the asymptotic behavior of the positive solution is investigated.

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Sofwah Ahmad, Mokhtar Kirane. 2025-02-20. Asymptotic behavior of solutions of a time-space fractional diffusive Volterra equation. https://arxiv.org/abs/2502.14725

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