[00104] High order approximation of Caputo-Prabhakar derivative and its application in solving time fractional Advection-Diffusion equation
Session Time & Room : 1E (Aug.21, 17:40-19:20) @E702
Type : Contributed Talk
Abstract : This work aims to devise a high-order numerical scheme to approximate the CaputoPrabhakar derivative of order 0 < α < 1, using an rth degree Lagrange interpolation polynomial, where $3\leq r\in\mathbb{Z^{+}}.$. This numerical scheme can be thought of as an extension of the presented schemes for the approximation of the Caputo-Prabhakar derivative in our previous work \cite{r1}. Further, we adopt the proposed scheme to solve a time-fractional Advection-Diffusion equation with the Dirichlet boundary condition. It is shown that the method is unconditionally stable, uniquely solvable, and convergent with convergence order, $ O(\tau^{r+1-\alpha}, h^{2}), $ where τ and h are the step sizes in the temporal and spatial directions, respectively. Without loss of generality, obtained results are supported by numerical examples for r = 4, 5.
\bibitem{r1} Deeksha Singh, Farheen Sultana, and Rajesh K Pandey, Approximation of Caputo Prabhakar derivative with application in solving time fractional advection-diffusion equation, International Journal for Numerical Methods in Fluids. $94(7)(2022)$, pp. 896-919.
