Lower and upper estimates of solutions to systems of delay dynamic equations on time scales

Successive approximations to solutions of dynamic equations on time scales

In this paper we establish the method of successive approximations within the field of “dynamic equations on time scales”. Our introduction and application of the method leads to new results concerning the qualitative and quantitative properties of solutions to nonlinear dynamic equations on time scales. The new discoveries include sufficient conditions under which we conclude: existence; uniqu...

On Lower and Upper Solutions without Ordering on Time Scales

In order to enlarge the set of boundary value problems on time scales, for which we can use the lower and upper solutions technique to get existence of solutions, we extend this method to the case when the pair lacks ordering. We use the degree theory and a priori estimates to obtain the existence of solutions for the second-order Dirichlet boundary value problems. To illustrate a wider applica...

Oscillation of Solutions to Impulsive Dynamic Equations on Time Scales

In this article, we study the oscillation of second order impulsive dynamic equations on time scales. The effect of the moments of impulse are fixed. Using Riccati transformation techniques, we obtain some conditions for the oscillation of all solutions

Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales

First order linear fuzzy dynamic equations on time scales

In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.