Calcium signaling is the requisite signaling process in most types of cells such as astrocytes, neurons, hepatocytes, cholangiocytes, etc. They regulate plenty of cellular activities in cholangiocyte cells that are responsible for the healthy signaling process. A dysregulation in the signaling process invites the pathogenesis of diseases and cholestatic disorders. The number of experimental studies reported in the past reveal the cellular mechanism and examine the role of various entities. Still, the precise role of each cellular entity in the cholangiocyte cell is poorly understood. Almost no mathematical attempt has been reported to examine the role of calcium in the cholangiocyte cell by fractional order approach. In the present study, a fractional order mathematical model is proposed for calcium dynamics and buffer to examine its role in the cholangiocyte cell. The necessary bio-physiological parameters are taken to develop a model in the form of a fractional reaction-diffusion model. The boundary and initial condition are framed as the physiological function of cholangiocyte cells. The model is simulated numerically for various physiological parameters and fractional order to validate the results and identify the precise role of the entity in the signaling process.