General Analytical Solutions to Fractional Differential Equations

This research introduces a new global technique for addressing fractional differential equations (FDEs), referred to as the N-Transform (NT). This method serves as a comprehensive integral transform, encompassing both Laplace and Sumudu transforms. A fixed point theorem is used to prove the existence and uniqueness of solutions. Finding general solutions to specific fractional differential equations and proving their uniqueness through the application of a fixed point theorem are the main goals of this study. The fractional derivatives are expressed in the Caputo framework. The findings indicate that this method is highly effective, straightforward, and applicable to differential equations across various fields of science.