This article aims at investigating stability properties for a class of discrete fractional equations with anti-periodic boundary conditions order \(\delta=(3,4]\). Utilizing Contraction mapping principle and fixed point theorem due to Brouwer, new criteria the uniqueness existence solutions are developed two types Ulam analysed. The theoretical outcomes corroborated examples.

due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. in this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on gurtin-murdoch continuum model to consider surface stre...