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We present the use of a Fourier transform on time scales to solve a dynamic heat IVP. This is done by inverting a certain exponential function via contour integral. We include some specific examples and directions for further study. [ABSTRACT FROM AUTHOR]

We obtain conditions for permanence and extinction of the infection for a nonautonomous SIQR model defined on an arbitrary time scale. The threshold conditions are given by some numbers that play the role of the basic reproduction number in this setting. As a particular case of our result, we recover several threshold conditions obtained in the literature, on discrete or continuous time, for autonomous, periodic models and general nonautonomous models and we also discuss some new situations, including an aperiodic time scale. [ABSTRACT FROM AUTHOR]

We establish some nonlinear integral inequalities for functions defined on a time scale. The results extend some previous Gronwall and Bihari type inequalities on time scales. Some examples of time scales for which our results can be applied are provided. An application to the qualitative analysis of a nonlinear dynamic equation is discussed. [ABSTRACT FROM AUTHOR]