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Mamadou Abdoul Diop

Publications and source records attributed to Mamadou Abdoul Diop.

5 recordsLinked to original sources
arXiv2026

Controllability of nonautonomous measure driven integrodifferential evolution equations with nonlocal conditions

This research delves into the exact controllability of semilinear measure-driven integrodifferential systems in nonlocal settings. We provide sufficient controllability requirements using the measure of noncompactness and the Mönch fixed point theorem without making any assumptions about how compact the evolution system is in relation to the linear part of the measure system. Here, we obtain results that both generalize and improve upon many prior findings.

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arXiv2026

Approximate Controllability of Nonlocal Stochastic Integrodifferential System in Hilbert Spaces

This project investigates the approximate controllability of a class of stochastic integrodifferential equations in Hilbert space with non-local beginning conditions. In a departure from the conventional concerns expressed in the literature, we will not consider compactness or the Lipschitz criteria concerning the nonlocal term. We use the fact that the resolvent operator is compact. We first prove the controllability of the nonlinear system using Schauder's fixed point theorem, a method known for its robustness; as well, we also use Grimmer's resolvent operator theory. Subsequently, we employ the reliable approximation methods and the powerful diagonal argument to determine the approximate controllability of the stochastic system. To conclude, we present an example that validates our theoretical statement.

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arXiv2025

Optimal Control of an Impulsive VS-EIAR Epidemic Model with Application to COVID-19

In this work, we investigate a VS-EIAR epidemiological model that incorporates vaccinated individuals $\{V_i : i = 1, \ldots, n\}$, where $n \in \mathbb{N}^{*}$. The dynamics of the VS-EIAR model are governed by a system of ordinary differential equations describing the evolution of vaccinated, susceptible, exposed, infected, asymptomatic, and deceased population groups. Our primary objective is to minimize the number of susceptible, exposed, infected, and asymptomatic individuals by administering vaccination doses to susceptible individuals and providing treatment to the infected population. To achieve this, we employ optimal control theory to regulate the epidemic dynamics within an optimal terminal time $τ^{*}$. Using Pontryagin's Maximum Principle (PMP), we establish the existence of an optimal control pair $(v^{*}(t), u^{*}(t))$. Additionally, we extend the model to an impulsive VS-EIAR framework, with particular emphasis on the impact of immigration and population movement. Finally, we present numerical simulations to validate the theoretical results and demonstrate their practical applicability.

math.DS↗
arXiv2024

Approximate Controllability for Nonautonomous Integrodifferential Equations with State-dependent Delay

We study the existence of mild solutions and the approximate controllability for nonautonomous integrodifferential equations with state-dependent delay. We assume the approximate controllability of the linear part, and then we use resolvent operator theory to prove the approximate controllability of the nonlinear case. An example of the one-dimensional heat equation with memory is given to illustrate the basic idea our results.

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