This paper proposes a fractional delay (FD) Newton structure for Lagrangian interpolation in single phase grid integrated photovoltaic (PV) system. The structure has been designed for achieving shunt compensation and as a phase locked loop circuit for synchronization. The designed controller performs multiple tasks of feeding the active power to meet the load demand and simultaneously providing reactive power compensation, power factor improvement, and compensating other power quality voltage and load current harmonics. Further, synchronization poses a severe challenge in integrating the PV power electronic converters to the grid. The FD filter is used to discretize the continuous time signal at any time instant using interpolation algorithm employing the non-integral value of the sampling rate delays. The FD delay filter is made adaptive and self-learning by using least mean square algorithm. The designed synchronization technique meets the objective of faithfully tracking the phase of the grid voltage under all grid disturbances such as under voltage, overvoltage, frequency variations, and phase angle disturbances in a precise manner.