The Directional Derivative in General Quantum Calculus

In this paper, we define the β-partial derivative as well β-directional of a multi-variable function based on β-difference operator, Dβ, which is defined by Dβf(t)=f(β(t))−f(t)/β(t)−t, where β strictly increasing continuous function. Some properties are proved. Furthermore, β-gradient vector and directional introduced. Finally, deduce Hahn-partial Hahn-directional derivatives associated with Hahn difference operator.