Solvability for a sequential system of random fractional differential equations of Hermite type

Abstract

In this work, we study the existence and uniqueness of solutions for a coupled problem of two-sequential random fractional differential equations. The considered problem allows us to obtain the classical Hermite random differential equation as a special case. Using the Banach contraction principle, we prove new existence and uniqueness results. New results on the Ulam-Hyers stability are also discussed.

Subject Classification: (2010):

• 30C45
• 39B72
• 39B82

Keywords:

• Caputo derivative
• Sequential random differential equation
• Coupled system
• Mean square solution
• Ulam stability
• Hermite random equation