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