The calcium signaling mechanism is the primary factor controlling the functions of \(\alpha \) -cells. Small deviations in calcium signaling patterns can lead to pathological conditions like diabetes, a widespread and intricate multifactorial condition. Therefore, a computational model has been developed to study such deviations. The present model describes the spatio-temporal intracellular calcium regulation of a single \(\alpha \) -cell. The primary objective of the study is to assess the impact of parameters associated with calcium signaling and how a minor disruption in the signaling pattern of these parameters can lead to disease conditions. To maintain the simplicity of the model, the major internal organelles like endoplasmic reticulum and mitochondria have been considered for the study, and the influx and efflux through the other organelles have been taken to be constant. The model also represents the Ca \(^{2+}\) dependent ATP production in normal and diabetic conditions. The model has been developed as a partial differential equation, incorporating both initial and boundary conditions that align with the physiological parameters of the \(\alpha \) -cell. Numerical solutions were obtained through simulation using the finite element and Crank–Nicolson methods. The error and the stability of the model have also been discussed at the end of the paper.