THE PROSPECTIVE ANALYSIS OF THREE-DIMENSIONAL TIME-FRACTIONAL HELMHOLTZ MODEL USING A NEW ITERATIVE METHOD

This work proposes a new iterative method (NIM) for the analytical examination of a three-dimensional time fractional Helmholtz problem with the appropriate initial conditions that arise in various natural models. We examine the concept of fractional operators by the means of Caputo order. The Sumudu transform (ST) is coupled with the homotopy perturbation method (HPM) to develop the concept of NIM. We present two numerical examples of fractional order to demonstrate the effectiveness and validity of the proposed technique. This research presents the relationship between the NIM results and the actual outcomes for the 3D fractional Helmholtz model. The NIM results indicate that as the terms of the series solution increase, the solution progressively aligns with the actual solution. The computed values specifically demonstrate that the approach for addressing fractional order problems in physical models is extremely precise and simple to comprehend.