  In this paper, we study the non-Newtonian version of C-algebras. Further, we
generalize some results which hold for the classical C-algebras. We also
discuss some illustrative examples to show accuracy and effectiveness of the
new findings. If we take the identity function I instead of the generators
{\alpha} and {\beta} in the construction of the set C(N), then non-Newtonian
C-algebras turn into the classical C-algebras, so our results are stronger than
some knowledge and facts in the most existing literature.
