Under the necessary compatibility condition and some mild regularity assumptions on the interior and the boundary data, we prove the existence, uniqueness, and

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.

This paper is designed to explore the asymptotic behaviour of a two dimensional visco-elastic plate equation with a logarithmic nonlinearity under the influence of nonlinear frictional damping. Assuming that relaxation function g satisfies g′(t)≤−ξ(t)G(g(t)), we establish an explicit general decay rates without imposing a restrictive growth assumption on the damping term. This general condition allows us to recover the exponential and polynomial rates. Our results improve and extend some existing results in the literature. We preform some numerical experiments to illustrate our theoretical results.

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