Existence and Uniqueness of solutions for fractional neutral stochastic delay differential equations

Abstract

Using the idea of step method, we discassed the existence and uniqueness of solutions of fractional neutral stochastic delay differential equations in the interval ［0,τ］,［τ,2τ］,…,［(n-1)τ,nτ］. Combining Picard iterative method and integral operator theory, we proved that the solutions of fractional neutral stochastic delay differential equations are in existence and unique. The conclusions in existing literature are generalized and improved.

Keywords

• neutral differential equation
• fractional order
• time delay
• existence and uniqueness
• integral operator