Some New Inequalities and Extremal Solutions of a Caputo–Fabrizio Fractional Bagley–Torvik Differential Equation

Abstract

This paper studies the existence of extremal solutions for a nonlinear boundary value problem of Bagley–Torvik differential equations involving the Caputo–Fabrizio-type fractional differential operator with a non-singular kernel. With the help of a new inequality with a Caputo–Fabrizio fractional differential operator, the main result is obtained by applying a monotone iterative technique coupled with upper and lower solutions. This paper concludes with an illustrative example.