Discovering the innumerable solutions of the (1 +1 ) -dimensional integro-differential Ito and (2 + 1 ) -dimensional integro-differential Sawda-Kotera equations via an efficient analytical technique

This research work demonstrates an approach to solve nonlinear evolution equations via the generalized \(\left(G{\prime }/G\right)\)-expansion method which is an advantageous mathematical tool for establishing abundant solutions of these types of nonlinear evolution equations. Here, we select the \(\left(1+1\right)\)-dimensional integro-differential Ito equation and \(\left(2+1\right)\)-dimensional integro-differential Sawda-Kotera equation to extract the closed traveling wave solutions by using the mentioned method. In applied Mathematics, mathematical Physics, engineering science as well as real time application fields have enormous application of these type of equations. The new traveling wave solutions derived by this method are involving hyperbolic function, trigonometric function and rational function. This method is direct, efficient, convenient and powerful to solve other nonlinear evolution equations. Moreover, the features of the solutions are illustrated by some figures.