Stochastic Chemotaxis Model with Fractional Derivative Driven by Multiplicative Noise

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 nonlinear Dirichlet boundary conditions, and disturbed multiplicative noise. The required results prove existence uniqueness mild solution time space-fractional, for use analysis techniques calculus semigroup theory, also studying regularity properties