On the single partial Caputo derivatives for functions of two variables

Abstract

In this work we propose definitions (distinguishable from the standard ones) of single partial derivatives in a Caputo sense of functions of two variables on the rectangle P=[0,a]times [0,b]. Next, we give an integral representation of functions possessing such derivatives. Finally, we apply these derivatives to the study of the existence and uniqueness of solutions and the continuous dependence of solutions on controls to a fractional counterpart of a nonlinear continuous Roesser type model.