Stochastic Chemotaxis Model with Fractional Derivative Driven by Multiplicative Noise

Abstract

We introduce stochastic model of chemotaxis by fractional Derivative generalizing the deterministic Keller Segel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. In this work, we study of nonlinear stochastic chemotaxis model with Dirichlet boundary conditions, fractional Derivative and disturbed by multiplicative noise. The required results prove the existence and uniqueness of mild solution to time and space-fractional, for this we use analysis techniques and fractional calculus and semigroup theory, also studying the regularity properties of mild solution for this model.

Analyzing election trends incorporating memory effect through a fractional-order mathematical modeling

“…In Addition, statistical methods [14] were incorporated into the fractional-order analysis using stochastic models. Slimani et al [15] published a paper on chemotaxis, a process in which cells move towards or away from chemical gradients. The authors developed a chemotaxis model with a fractional derivative and multiplicative noise to simulate the random motion of cells, whereas Azizi's paper discusses the application of fractional calculus to pharmacokinetic compartmental modeling [16].…”

Existence and uniqueness of solution for a fractional thixotropic model

“…In this part, we study the convergence of the problem $$$ \left({P}^{\prime}\right) $$$ to the problem $$$ (P) $$$; this study is based on the Banach fixed point theorem [27].…”

Analytical Solution of One-Dimensional Keller-Segel Equations via New Homotopy Perturbation Method

“…Chemotaxis is represented by a model to explain the chemotaxis phenomenon, a chemical attraction that exists between organisms. Among the most important works accomplished for this phenomenon, we mention [30][31][32].…”