Study and Analysis of Taylor’s Series using The Modified Conformable Operator

In this paper, we explore an essential concept in mathematics: Taylor’s series. To examine its behavior in fractional calculus, we utilize the modified conformable operator, which provides significant results by satisfying most properties of the classical derivative and establishing a strong connection between the usual and fractional derivatives. We then present theoretical results for the fractional Taylor series using the proposed operator. Finally, we demonstrate the effectiveness of this approach through numerical examples and simulations in Mathematica, which validate the obtained results.