Nonlinear Random Differential Equations with n Sequential Fractional Derivatives

Abstract

This article deals with a solvability for a problem of random fractional differential equations with n sequential derivatives and nonlocal conditions. The existence and uniqueness of solutions for the problem is obtained by using Banach contraction principle. New random data concepts for the considered problem are introduced and some related definitions are given. Also, some results related to the dependance on the introduced data are established for both random and deterministic cases.

Keywords

• mean square caputo derivative
• random differential equation
• existence and uniqueness
• nonlocal condition
• sequential fractional differential equation
• 30c45
• 39b72
• 39b82