arXiv subjects

Sofwah Ahmad

Publications and source records attributed to Sofwah Ahmad.

3 recordsLinked to original sources

arXiv2026

The regional control of a fractional spatio-temporal SIR model

This paper investigates a regional optimal control problem for a nonlinear spatio-temporal epidemiological model involving fractional diffusion on a bounded domain. In this work, we consider a general form of disease transmission, and two types of control, vaccination and treatment. We establish the existence and uniqueness of global-in-time solutions to our proposed system. We also prove the existence of an optimal control that minimizes the infected individuals as well as the cost of vaccination and treatment. The necessary conditions for optimality are derived. We show that concentrating vaccination in a selected region of the domain can substantially mitigate the spread of the disease. Numerical simulations are given.

math.AP↗

arXiv2025

Tools for stability analysis of fractional reaction diffusion systems

The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we prove this principle for solutions of abstract fractional reaction-diffusion equations with a fractional derivative in time of order $α\in (0,1)$. Then, we apply these results to particular fractional reaction-diffusion equations, obtaining, for example, the counterpart of the classical Turing instability in the case of fractional equations.

math.AP↗

arXiv2025

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

In this paper, we study the time-space fractional differential equation of the Volterra type: \begin{align*} {D}^α_{0 \vert t} (u) +(-Δ_N)^σu &= u(1+au-bu^2)-au\int_0^t {K}(t-s) u(\cdot) \, ds, \end{align*} where $a,b>0$ are given constants, $α,σ\in (0,1)$, 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.

math.AP↗