Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay

Abstract

In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carathéodory approximation approach and stochastic calculus to present the existence and uniqueness theorem of the stochastic system under Carathéodory-type conditions with Lipschitz and non-Lipschitz conditions as special cases. Some existing results are generalized and enhanced. Finally, an application is offered to illustrate the obtained theoretical results.

Keywords

• fractional differential system of neutral type
• fractional brownian motion
• fractional calculus
• Poisson jump
• Carathéodory approximation