Volterra theory on time scales
Time scales theory was introduced by \textit{S. Hilger} [Result. Math. 18, No. 1--2, 18--56 (1990; Zbl 0722.39001)]. The objective of this theory is to unify the discrete and the differential calculus. This paper addresses generalized Volterra integral equations on time scales. It is reported that the continuity property can be relaxed for the kernel function. That is because the author employs the method to guarantee existence and uniqueness which does not make use of the Banach fixed-point theorem. For more results on the Volterra equations with piecewise continuous kernels, the readers may refer to \textit{D. N. Sidorov} [Differ. Equ. 49, No. 2, 210--216 (2013); translation from Differ. Uravn. 49, No. 2, 209--215 (2013; Zbl 1348.45002)]. The paper also covers results concerning the reciprocity property of kernels and Picard iterates.
scientific article; zbMATH DE number 6305232
scientific article