We extend some Hardy-type inequalities with general kernels to arbitrary time scales using multivariable convex functions. Some classical and new inequalities are deduced seeking applications.

Abstract. In this paper, we extend some Hardy-type inequalities with certain kernels to arbitrary time scales. Certain classical and some new integral and discrete inequalities are deduced in seek of applications.Mathematics subject classification (2010): 26D15, 34N05, 28A25.

This paper is dedicated to Opial-type inequalities for arbitrary kernels using convex functions. These inequalities are further applied to a power function. Applications of the presented results are studied in fractional calculus via fractional integral operators by associating special kernels.

We study the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions of the following system of exponential difference equations:, where the parameters , , , , , and for ∈ {1, 2} and initial conditions 0 , −1 , 0 , and −1 are positive real numbers. Furthermore, by constructing a discrete Lyapunov function, we obtain the global asymptotic stability of the positive equilibrium. Some numerical examples are given to verify our theoretical results. Hindawi Publishing Corporation