In this piece of research, our aim is to investigate the novel solitons solutions of nonlinear (4+1)-dimensional Fokas equation (FE) and (2+1)-dimensional Breaking soliton equation (BSE) via new extended direct algebraic method. New acquired solutions are bright, singular, dark, periodic singular, combined-dark bright and combined-dark singular solitons solutions along with hyperbolic and trigonometric functions solutions. The achieved distinct types of solitons solutions contain key applications in engineering and physics. By taking the appropriate values of involved parameters, numerous novel structures are also plotted. These solutions define the wave performance of the governing models, actually.

In this work, we prove Ostrowski-Mercer inequalities for differentiable harmonically convex functions. It is also shown that the newly proved inequalities can be converted into some existing inequalities. Furthermore, it is provided that how the newly discovered inequalities can be applied to special means of real numbers.

This paper deals with mathematical analysis of a generalized fractional alcoholic model. The present model is constructed by the Atangana-Baleanu fractional operator with the memory function, which is utilized for the generalization of alcoholic model. The used memory function provides the information on entire domain of model except the initial stage. The existence of solution is veried by Picard iterative method and uniqueness of solution is also proved.