INTRODUCING THE NEW INTEGRAL TRANSFORMATION TO SOLVE FRACTIONAL DIFFERENTIAL EQUATIONS

To differentiate itself from other integral transformations, this article presents a novel integral transformation known as the A (or Aman) transform. This transformation was inspired by a thorough study of the effectiveness of the Laplace and Sumudu transforms, specifically with regard to fractional differential equations. Applying these transformations might occasionally make processing their inverse transform challenging. This concept encourages us to reconsider and put in more effort to develop fresh, essential transformations that will make difficult problems easier to tackle. The proposed transformation has been successfully used to solve the Riemann-Liouville and Caputo FDE analytically. The outcomes of using this new approach are in perfect harmony with those of using contemporary methods. This demonstrates the A transform's dependability and efficiency in the analytical resolution of complex mathematical situations