EXISTENCE RESULTS FOR BOUNDARY VALUE PROBLEMS OF VOLTERRA-FREDHOLM SYSTEM INVOLVING CAPUTO DERIVATIVE

Abstract

In this study, a class of nonlinear boundary fractional Caputo Volterra-Fredholm integro-differential equations (CV-FIDEs) is taken into account. Under specific assumptions about the available data, we firstly demonstrate the existence and uniqueness features of the solution. The Gronwall’s inequality, a adequate singular  Hölder's inequality, and the fixed point theorem using an a priori estimate procedure. Finally, a case study is provided to highlight the findings.