Existence, uniqueness and continuous dependence of solution to random delay differential equation of fractional order

Document Type : Research Paper


Faculty of Mathematical Economics, Ho Chi Minh University of Banking, Vietnam


In this paper, we aim to prove the existence, uniqueness of the solution to the random delay differential equation of fractional order involving the successive approximation method. Moreover, using the Gronwall inequality, we study the continuous dependence of solution in the mean square sense of the problem. Finally, the fractional $\epsilon$-approximate solution in the mean square sense is also considered.


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Volume 13, Issue 2
July 2022
Pages 447-457
  • Receive Date: 07 December 2021
  • Revise Date: 14 April 2022
  • Accept Date: 02 May 2022