On new evolution of Ri’s result via <italic>w</italic>-distances and the study on the solution for nonlinear integral equations and fractional differential equations.

The aim of this work is to establish a new fixed point theorem for generalized contraction mappings with respect to <italic>w</italic>-distances in complete metric spaces. An illustrative example is provided to advocate the usability of our results. Also, we give a numerical experiment for approximating a fixed point in these examples. As an application, the received results are used to summarize the existence and uniqueness of the solution for nonlinear integral equations and nonlinear fractional differential equations of Caputo type. [ABSTRACT FROM AUTHOR]