Superpositions of Functions with Fractal Properties

We study structural, integral, differential, variational, and fractal properties of a function f whose argument $$ x={\Delta }_{\alpha_1{\alpha}_2\dots {\alpha}_n\dots}^{Q_s^{\ast }} is represented by polybasic s-symbol {Q}_s^{\ast } -representation (1 < s ∈ N) its corresponding value expressed as follows: f\left(x={\Delta }}\right)={a}^{\alpha_1{u}_1+{\alpha}_2{u}_2+\dots +{\alpha}_n{u}_n+\dots }, where u1 + u2 … given convergent positive series αn {0, 1, …, - 1}.