Calcium oscillation occurs due to the concentration gradient of the calcium ion in the neuronal soma. Cellular calcium ions are mediated by the different organelles and other physiological parameters. This oscillation is led by different interactions between organelles and soma, where a major portion is covered by the endoplasmic reticulum (ER) which interacts with Orai interaction according to its calcium level. Also, Sarcoendoplasmic Reticulum Calcium ATPase (SERCA) fills up the ER to maintain calcium concentration. Both of these parameters complexify the real-world problem of neuronal cells. Increasing abnormality of the physiology could lead to alteration in the neuron and may cause neuronal disorders like Alzheimer’s disease. To investigate these physiological phenomena mathematically a time fractional reaction-diffusion model is developed, where the reaction-diffusion approach incorporates the calcium buffering process. To solve this model, we have used the integral transform method. The significant effect of these parameters on cytosolic calcium concentration is shown graphically under neuronal abnormality.