In this paper  introduced the concept σ-Differentiability over a locally convex algebra A (breifly(A,σ)-Differentiability) of mappings constructed by a system of bounded subsets in a convex algebra, and also created σ-continuous and (A,σ)-continuous mappings in these algebras, demonstrating their linearity and continuity. Specifically, We offer a novel approach to differentiability in topological algebras endowed with a locally convex topology by extending the method of V.I. Averbuch and O.G. Smolyanov in [3].