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In this article, we study and implement a relatively new analytical technique called q-Homotopy Analysis Method on the strongly nonlinear fractional BBM-Burger's equations with dissipative term. We obtain analytically, approximate solutions with two different initial conditions in the form of convergent series with easily computable components. For some special cases on the coefficient of the dissipative term, comparison is made with the exact solution and the solution obtained using other existing analytical methods. Our numerical analysis shows that this method is easy to implement and accurate when applied to strongly nonlinear partial (fractional) differential equations due to the presence of the auxiliary parameter h and the fraction factor.

Recently, Ferrero and Gazzola, [Disc. Cont. Dyn. Syst. 35: 5879–5908 (2015)], suggested and investigated a rectangular plate model describing the statics and dynamics of a suspension bridge. The plate is assumed to be hinged on its vertical edges and free on its remaining horizontal edges. This reliable model aims to describe more accurately the motion of suspension bridges compared to all previous known models. In the present paper, we consider a plate equation in the presence of memory and subject to the above‐mentioned boundary conditions. We give a rigorous well‐posedness result and establish the existence of a global attractor.

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