Abstract:
In this project, we are interested to study random fractional di erential
equations. They are de ned as fractional di erential equations
involving second order random/stochastic elements for that we use the
ideas of the fractional calculus to a mean-square setting.
We introduce a new class of problems for random fractional di erential
equations. The existence and uniqueness of random solutions is rst
obtained by means of appropriate xed point theorems. New concepts
on the sequential continuous and fractional derivative dependence are
introduced. Some examples are discussed to illustrate our main results.
Then, a class of random di erential equations of Airy type is introduced.
The existence and uniqueness criterion for stochastic process
solutions for the introduced class is discussed. New concepts and notions
on di erential dependence are also introduced and some related
results are proved. Several illustrative examples are given at the
end
