On the existence of solution for fractional differential equations of order 3< δ1≤4

Abstract

In this paper, we deal with a fractional differential equation of order δ1∈(3,4] with initial and boundary conditions, (Formula Presented), addressing the existence of a positive solution (EPS), where the fractional derivatives Dδ1, Dα1 are in the Riemann-Liouville sense of the order δ1, α1, respectively. The function (Formula Presented). To this aim, we establish an equivalent integral form of the problem with the help of a Green’s function. We also investigate the properties of the Green’s function in the paper which we utilize in our main result for the EPS of the problem. Results for the existence of solutions are obtained with the help of some classical results.