Applications of B-spline in Fractional Partial Differential Equations

Abstract

The fractional derivatives have a significantly greater rate of resistance in the model for characterizing the history of variable and its features in a variety of dynamical systems. The fractional partial differential equation (FPDE) will be considered in the singular and nonsingular kernel. For the time direction, we will use singular kernel as well as non-singular kernel and for spatial direction, we are using exponential B-spline. In this thesis we presents a numerical methodology for a class of time-fractional reaction- diffusion equations using the exponential B-spline method.The time-fractional reaction-diffusion (TFRD) model offers broad physical views and theoretical interpretations, and its numerical approaches are important both conceptually and practically. A numerical approach for solving the TFRD model with the singular kernel as well as non-singular kernel is developed. The Caputo derivative operator as well as Caputo-Fabrizio operator is used to discretize time levels, while the exponential B- spline function is used to discretize space direction. In order to check the efficiency of the techniques, the stability analysis have been analyzed which is unconditional stabile. Several numerical examples are provided to demonstrate the proposed scheme’s feasibility and efficiency.