Technique for solving the Bagley-Torvik equation via integer-order differential equations

Abstract EN

This paper proposes an analytical technique for solving the Bagley-Torvik equation (BTE) in the Caputo sense.

The main idea of this technique is based on reformulating the considered problem as a system of linear FDEs of half-order.

Then the resulting system is transformed into a set of integer-order differential equations.

In such a transformation, the singularity terms are removed from the FDE system.

So, the solution of the BTE can be obtained via solving this system.

Finally, two examples are given to demonstrate the efficiency of the proposed technique.