Two fractional derivative inclusion problems via integral boundary condition

Abstract

The goal of the manuscript is to analyze the existence of solutions for the Caputo fractional differential inclusion (c)D(q)x(t) is an element of F(t,x(t), (c)D(beta)x(t)) with the boundary value conditions x(0) = 0 and x(1) + x'(1) = integral(eta)(0) x(s)ds, such that 0 < eta < 1, 1 < q <= 2, 0 < beta < 1 and q = beta > 1. Also, we investigate the existence of solutions for the Caputo fractional differential inclusion (c)D(q)x(t) is an element of F(t,x(t)) such that x(0) = a integral(nu)(0) x(s)ds and x(1) = b integral(eta)(0) x(s)ds, where 0 < nu, eta < 1, 1 < q <= 2 and a, b is an element of R