in recent years, numerous approaches have been applied for finding the solutions of functional equations. one of them is the optimal homotopy asymptotic method. in current paper, this method has been applied for obtaining the approximate solution of fisher equation. the reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...

We present a general method for constructing real solutions to some problems in enumerative geometry which gives lower bounds on the maximum number of real solutions. We apply this method to show that two new classes of enumerative geometric problems on flag manifolds may have all their solutions be real and modify this method to show that another class may have no real solutions, which is a ne...

Relations between the string topology of Chas and Sullivan and the homotopy skein modules of Hoste and Przytycki are studied. This provides new insight into the structure of homotopy skein modules and their meaning in the framework of quantum topology. Our results can be considered as weak extensions to all orientable 3-manifolds of classical results by Turaev and Goldman concerning intersectio...

This article aims at preferring a new and viable algorithm, specifically a two-step homotopy perturbation transform algorithm (TSHPTA). This novel technique is a feasible way in finding exact solutions with a small amount of calculations. As a simple but typical example, it demonstrates the strength and the great potential of the two-step homotopy perturbation transform method to solve nonlinea...

The authors have used generalised Galois Theory to construct a homotopy double groupoid of a surjective fibration of Kan simplicial sets. Here we apply this to construct a new homotopy double groupoid of a map of spaces, which includes constructions by others of a 2-groupoid, cat-group or crossed module. An advantage of our construction is that the double groupoid can give an algebraic model of...

Abstract: In this paper, new algorithm of homotopy analysis method is successfully applied to obtain the approximate analytical solutions of the Cauchy reaction-diffusion equation. Reaction-diffusion equations have special importance in engineering and sciences and constitute a good model for many systems in various fields. Application of new algorithm of homotopy analysis method to this proble...

The present work introduces an effective modification of homotopy perturbation method for the solution of nonlinear time-fractional biological population model and a system of three nonlinear time-fractional partial differential equations. In this approach, the solution is considered a series expansion that converges to the nonlinear problem. The new approximate analytical procedure depends onl...