A study on the exact controllability of neutral fractional differential equations with Hilfer-Katugampola fractional derivatives

In this study, we investigate the existence of mild solutions and the exact controllability of Hilfer–Katugampola fractional neutral differential equations involving almost sectorial operators. We first establish the existence of mild solutions and then demonstrate the exact controllability of the proposed system. The existence results are obtained by employing techniques from fractional calculus, semigroup theory, Katugampola fractional integrals and derivatives, and the Laplace transform. Furthermore, a theoretical example is presented to illustrate the obtained results.