Volterra Integral Equations Governed by Highly Oscillatory Functions on Time Scales

It is well known that there are many analogies between the theories of difference equations and differential equations. The concept of time scales unifies these two situations but gives also solutions for problems on discrete sets with non-uniform step size or combinations of real and discrete intervals and many others. On the other hand, as it was seen in literature (beginning with [2]), the study of dynamical systems leads, in a very natural way, to integrals of highly oscillatory functions, such as the Henstock-type integrals. On time scales, integrals of this type were introduced on the real line in [16] and [3] and in general Banach spaces in [8] and, recently, used in applications (see [9]). Combining methods used in both theories (time scales and non-absolute