Solvability of fuzzy fractional stochastic Pantograph differential system

In this paper, a new type of  equation namely  fuzzy fractional stochastic Pantograph delay differential system  (FSPDDS) is proposed. In our previous work,  a first  extension of fuzzy stochastic differential system into   fuzzy fractional stochastic differential system by using Granular differentiability has been established. Here we study the existence and uniqueness  results for the fuzzy FSPDDS which  are obtained by using  generalized Granular  differentiability  and contraction principle with weaker conditions. This kind of equation is used in many real world problems. Finally, we provide two numerical examples for the effectiveness of the theoretical results.

Keywords:

Banach contraction , fuzzy fractional , fuzzy stochastic , granular differentiability