Sensitive visualization of the fractional wazwaz-benjamin-bona-mahony equation with fractional derivatives: A comparative analysis

Abstract In this paper, we interrogate the optical soliton solutions of three-dimensional fractional Wazwaz Benjamin Bona Mahony (WBBM) equation. With a new auxiliary equation scheme, we form the solitary wave solitons of the considered model. By using this methodology, the acquired solutions conduct a range of the new families. These new classes of solutions include bright, dark, dark-bright, dark singular, singular and unique solutions. The predicted solutions are yielded with constraint conditions and portrayed through 2D and 3D plots by taking suitable values of parameters. There is a comparative study being showed among the two proposed definitions of Beta and the Atangana-Baleanu fractional derivatives. A comprehensive sensitivity analysis of the WBBM equation is mentioned. There is also a quantitative overview including its solutions to the problem under consideration, derived using different interpretations of derivative.