A Fractional α-Transform for Solving Second-Order Fractional Differential Equations: A New Insight

Fractional Differential Equation (FDE) plays a powerful role in the applications of applied science and engineering. In this paper, the α-fractional transform has been used to convert FDE to ordinary differential equations (ODEs). A new α-transform has been developed using the features of the special version of the α-fractional derivative for real functions. Studies demonstrated that this definition's elements are appropriate, relevant, and useful in solving FDEs and their applications. The proposed α-transform approach was used to convert the FDE to an ODE. Also, some of the examples of second-order FDEs are solved using this proposed method. This study presented the α-transform approach, which has been used for dealing with a number of FDE issues. Therefore, the examples show that the α-transform technique is the most cost-efficient and efficient method for converting FDEs into ODEs.