Open AccessStochastic Chemotaxis Model with Fractional Derivative Driven by Multiplicative Noise
Author(s) -
Ali Slimani,
Amira Rahai,
Amar Guesmia,
Lamine Bouzettouta
Publication year - 2021
Publication title -
international journal of analysis and applications
Language(s) - English
Resource type - Journals
ISSN - 2291-8639
DOI - 10.28924/2291-8639-19-2021-858
Subject(s) - mathematics , fractional calculus , multiplicative function , uniqueness , multiplicative noise , semigroup , chemotaxis , mathematical analysis , computer science , signal transfer function , digital signal processing , analog signal , biochemistry , chemistry , receptor , computer hardware
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.