fuzzy q-taylor theorem

The main purpose of this work is to introduce and investigate fuzzy quantum calculus. our idea begins with a general definition of fuzzy q-derivative on arbitrary time scales using the generalized hukuhara difference. it compiled some basic facts in the fields of the fuzzy q-derivative and the fuzzy q-integral and proved them in detail. proceed with this work, specifying the particular concept of fuzzy q-taylor’s expansion, especially for continuous and fuzzy valued functions which are non-differentiable in the classical (usual) concept, as the best tool for approximating functions and solving the fuzzy initial value q-problems. eventually, some numerical examples of fuzzy q-taylor’s expansion of special functions and functions with switching points, are solved for illustration.