An Efficient Numerical Scheme for Fractional Order Mathematical Model of Cytosolic Calcium Ion in Astrocytes

Abstract

The major aim of this article is to obtain the numerical solution of a fractional mathematical model with a nonsingular kernel for thrombin receptor activation in calcium signals using two numerical schemes based on the collocation techniques. We present the computational solution of the considered fractional model using the Laguerre collocation method (LCM) and Jacobi collocation method (JCM). An operational matrix of the fractional order derivative in the Caputo sense is needed for the recommended approach. The computational scheme converts fractional differential equations (FDEs) into an algebraic set of equations using the collocation method. The technique is used more quickly and successfully than in other existing schemes. A comparison between LCM and JCM is also presented in the form of figures. We obtained very good results with a great agreement between both the schemes. Additionally, an error analysis of the suggested procedures is provided.