Soliton solutions of the time-fractional Sharma–Tasso–Olver equations arise in nonlinear optics

This article focuses on the investigation of the time-fractional Sharma–Tasso–Olver equation, a crucial equation with significant relevance in various scientific domains, including nonlinear optics, quantum field theory, and the physical sciences. The natural transform decomposition approach, an efficient and innovative methodology, is used in this study. The two nonsingular kernel derivatives, such as Caputo–Fabrizio and Atangana–Baleanu in the Caputo sense, are used in the suggested technique. We considered two nonlinear cases with suitable initial conditions to show that the proposed method is accurate and works well with the existing methods. Banach’s fixed point theorem is used to demonstrate the uniqueness and convergence of the solution that has been achieved. The proposed solution accurately captures the behaviour of the reported findings for various fractional orders. The obtained outcomes of the suggested approach are contrasted with those of the precise solution and other numerical techniques, including the natural transform decomposition method with Caputo derivative, the natural transform iterative method, the q-homotopy analysis Elzaki transform method, and the fractional reduced differential transform method. The outcomes of the proposed method are presented in tables and figures. The findings of this study demonstrate that the investigated technique is highly effective and precise in solving nonlinear time fractional differential equations.