Analysis and Applications of Composed Forms of Caputo Fractional Derivatives

In this paper we consider two ordinary fractional differential equations with composition of the left and the right Caputo derivatives. Analytical solution of this type of equations is known for particular cases, having a complex form, and therefore is difficult in practical calculations. Here, we present two numerical schemes being dependent on a fractional order of equation. The results of numerical calculations are compared with analytical solutions and then we illustrate convergence of our schemes. Finally, we show an application of the considered equation.