Toward solving fractional differential equations via solving ordinary differential equations

In the present paper, we successfully solve some linear fractional differential equations (FDE) analytically by solving an auxiliary linear differential equation with an integer order. The idea of the suggested method is based on transforming the given FDE into a linear differential equation with an integer order. This transformation removes certain terms of the solution of the considered FDE, resulting in the remaining terms being a solution to the auxiliary equation. To demonstrate the ability and efficacy of this idea, several examples have been provided.

Automated summary

In this paper, we successfully solve some linear fractional differential equations (FDE) analytically by transforming them into linear differential equations with integer orders. By solving an auxiliary linear differential equation, certain terms of the original FDE are eliminated, resulting in the remaining terms being a solution to the auxiliary equation. Several examples are provided to demonstrate the ability and efficacy of this method.