Existence of solutions to Caputo fractional differential inclusions of 1 < & alpha; < 2 with initial and impulsive boundary conditions

This paper is concerned with the existence of solutions to the Caputo fractional differential inclusion of 1 < & alpha; < 2 with initial and impulsive boundary conditions. A novel existence result is presented based on the fixed-point theorem of Dhage for multi-valued operators with some assumptions. Finally, two examples are provided to explicate the applicability of the main result.