Aminu Ma'ARuf Nass

This paper uses Lie symmetry analysis to investigate the biharmonic heat equation on a generalized surface of revolution. We classify the Lie point symmetries associated with this equation, allowing for the identification of surfaces and the corresponding infinitesimal generators. In a significant move, we demonstrate that the biharmonic heat equation on a surface of revolution admits the same Lie symmetries as the harmonic heat equation on the same surface, highlighting a profound structural relationship between the two equations. Utilizing these symmetry groups, we derive similarity reductions that yield invariant forms of the equation and facilitate the construction of exact solutions. Finally, we provide certain examples illustrating precise solutions on the related surfaces with positive, negative, and zero Gaussian curvatures, demonstrating the versatility of the approach. This work contributes to the understanding of biharmonic heat equations on symmetric surfaces.

A fractional order system of evolution partial differential equations with a constant delay is considered. By exploiting the Lie symmetry method, we give a complete group classification of the system. Furthermore, we establish the corresponding symmetry reductions and construct some analytical solutions to the system.

In this article, we discussed the Lie symmetry analysis of fractional and integer order differential equations. The symmetry algebra of both differential equations is obtained and utilized to find the similarity reductions, invariant solutions, and conservation laws. In both cases, the symmetry algebra is of low dimensions.

In the present work, we study a one-dimensional laminated Timoshenko beam with a single nonlinear structural damping due to interfacial slip. We use the multiplier method and some properties of convex functions to establish an explicit and general decay result. Interestingly, the result is established without any additional internal or boundary damping term and without imposing any restrictive growth assumption on the nonlinear term, provided the wave speeds of the first equations of the system are equal.

The fractional partial differential equations have wide applications in science and engineering. In this paper, the Kudryashov techniques were utilized to obtain an exact solution of both fractional generalized equal width (GEW)-Burgers and classical GEW-Burgers equations. The general analytical solutions of the two partial differential equations are constructed for n>1. The graphical representation of the solutions is given in comparison with some previous results in the literature. The advantages and disadvantages of the method were listed.