No abstract

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.

The existence, uniqueness and continuous dependence of a mild solution of a Cauchy problem for semilinear impulsive first and second orderfunctional differential-equations with nonlocal conditions in general Banach spaces are studied. Methods of fixed point theorems, of a C0 semigroup of operators and the Banach contraction theorem are applied

Abstract-The purpose of this paper is to investigate the global exponential stability of a class of impulsive bidirectional associative memories (BAM) neural networks that possesses Cohen-Grossberg dynamics. By constructing and using some inequality techniques and a fixed point theorem sufficient conditions are obtained to ensure the existence and global exponential stability of the solutions for impulsive Cohen-Grossberg neural networks with time delays and distributed delays.