The Novel Study on the Benjamin–Bona–Mahony Equation with Conformable Fractional Operator

In this study, the conformable fractional Benjamin–Bona–Mahony (BBM) equation is solved by using the conformable q-formable homotopy analysis transform method (Cq-FHATM). This paper presents a practical implementation that demonstrates the possible advantages and effectiveness of the stated approach. In addition, an error analysis is undertaken to validate the scheme\\\'s precision. The accuracy of the method in the study is ensured by computational simulations. This study shows the findings obtained from numerical and graphical analysis. It also explains a computationally accurate and simple strategy to understand and solve complex phenomena in science and technology using compatible fractional nonlinear partial differential equations.