Two fractional derivative inclusion problems via integral boundary condition

- We analyze the existence of solutions for the Caputo fractional differential inclusion.
- Two types of integral boundary conditions were considered.
- Recent fixed point results were used to resolve the inclusion problems.

The goal of the manuscript is to analyze the existence of solutions for the Caputo fractional differential inclusion cDqx(t)∈F(t,x(t),cDβx(t)) with the boundary value conditions x(0)=0 and x(1)+x′(1)=∫0ηx(s)ds, such that 0<η<1, 11. Also, we investigate the existence of solutions for the Caputo fractional differential inclusion cDqx(t)∈F(t,x(t)) such that x(0)=a∫0νx(s)ds and x(1)=b∫0ηx(s)ds, where 0<ν, η<1, 1