Caputo-Katugampola-type implicit fractional differential equation with anti-periodic boundary conditions

Abstract

The given article describes the implicit fractional dierential equation with anti-periodic boundary conditionsin the frame of Caputo-Katugampola fractional derivative. We obtain an analogous integral equation of thegiven problem and prove the existence and uniqueness results of such a problem using the Banach andKrasnoselskii xed point theorems. Further, by applying generalized Gronwall inequality, the Ulam-Hyersstability results are discussed. To show the eectiveness of the acquired results, convenient examples arepresented.