The q-derivative and differential equation

The q-calculus appeared as a connection between mathematics and physics. It has several applications in different mathematical areas such as number theory, combinatorics, orthogonal polynomials, basic hypergeometric functions, quantum theory, and electronics. Recently, a great interest to its applications in differential transform methods, in order to get analytical approximate solutions to the ordinary as well as partial differential equations. In this paper, we present some of the interesting definitions of q-calculus and q-derivatives. By using q-calculus, solutions of some differential equations could be generated. (paper)