Abstract
A free calcium ion in the cytosol is essential for many physiological and physical functions. Also, it is known as a second messenger as the quantity of free calcium ions is an essential part of brain signaling. In this work, we have attempted to study calcium signaling in the presence of mitochondria, buffer, and endoplasmic reticulum fluxes. Small organelles called mitochondria are found in the nervous system and are involved in several cellular functions, including energy production, response to stress, calcium homeostasis regulation, and pathways leading to cell death. It has been discovered that buffer, endoplasmic reticulum, and mitochondria significantly affect calcium signaling. To investigate how various circumstances impact the quantity of calcium in the cytosol, a mathematical model of a second-order linear partial differential equation with fuzzy boundary conditions has been developed. Systems having ambiguous or imprecise boundary values can be effectively modeled and simulated with the help of fuzzy boundary conditions. Models can provide more dependable and instructive outcomes and become adaptable to real-world circumstances by implementing fuzzy logic into boundary conditions. In this paper, we observed the Fuzzy Laplace Transform to solve variable coefficient fuzzy differential equations using triangular fuzzy numbers. It is noted that maintaining the delicate calcium ion balance, which controls essential cellular functions, depends on the buffer affinity. Also, neurodegenerative illnesses like Alzheimer's, Parkinson's, etc. are linked to disruptions in the control of components such as buffers, mitochondria, and the endoplasmic reticulum.