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.
In this work, we study the existence and uniqueness of solutions of the fractional thixotropic problem
in one‐dimensional case. The problem of thixotropic was studied by many researchers. But our study is focussed on the fractional derivative
, which is a new addition to the previous works of thixotropic problem. So, in this work, we based on two parts: The first is studding the existence and uniqueness of solutions of the modified fractional thixotropic model
using regularization, some prior estimates, and Gronwall's lemma. The second is proving that the problem
converges to the fractional thixotropic model
by using fixed point theorem.
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