On Cauchy Problems of Caputo Fractional Differential Inclusion with an Application to Fractional Non-Smooth Systems

Abstract

In this innovative study, we investigate the properties of existence and uniqueness of solutions to initial value problem of Caputo fractional differential inclusion. In the study of existence problems, we considered the case of convex and non-convex multivalued maps. We obtained the existence results for both cases by means of the appropriate fixed point theorem. Furthermore, the uniqueness corresponding to both cases was also determined. Finally, we took a non-smooth system, the modified Murali–Lakshmanan–Chua (MLC) fractional-order circuit system, as an example to verify its existence and uniqueness conditions, and through several sets of simulation results, we discuss the implications.

Keywords

• fractional differential inclusions
• initial value problem
• Caputo fractional derivative
• fractional non-smooth system
• fixed point theorem
• nonlinear equations