Random Fractional Di erential Equations and Applications

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