  The fractional q-calculus is the q-extension of the ordinary fractional
calculus and dates back to early 20-th century. The theory of q-calculus
operators are used in various areas of science such as ordinary fractional
calculus, optimal control, q-difference and q-integral equations, and also in
the geometric function theory of complex analysis. In this article, for the
first time, we apply certain q-calculus operators to complex harmonic functions
and obtain sharp coefficient bounds, distortion theorems and covering results.
