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A new extended cubic B-spline (ECBS) approximation is formulated, analyzed and applied to obtain the numerical solution of the time fractional Klein–Gordon equation. The temporal fractional derivative is estimated using Caputo's discretization and the space derivative is discretized by ECBS basis functions. A combination of Caputo's fractional derivative and the new approximation of ECBS together with 𝜃 -weighted scheme is utilized to obtain the solution. The method is shown to be unconditionally stable and convergent. Numerical examples indicate that the obtained results compare well with other numerical results available in the literature. [ABSTRACT FROM AUTHOR]

A finite difference scheme which depends on a new approximation based on an extended cubic B-spline for the second order derivative is used to calculate the numerical outcomes of time fractional Burgers equation. The presented scheme uses Caputo's formulation for the time derivative. Finite difference method will be used to discretize the Caputo's fractional derivative. The proposed scheme will be shown to be unconditionally stable by Von-Neumann method. The convergence analysis of the numerical scheme will be presented of order O (h 2 + τ 2 - α). The presented scheme is tested on four numerical examples. The numerical results are compared favorably with other computational schemes. [ABSTRACT FROM AUTHOR]