An efficient spline technique for solving time-fractional integro-differential equations.

Spline curves are very prominent in the mathematics due to their simple construction, accuracy of assessment and ability to approximate complicated structures into interactive curved designs. A spline is a smooth piece-wise polynomial function. The primary goal of this study is to use extended cubic B-spline (ExCuBS) functions with a new second order derivative approximation to obtain the numerical solution of the weakly singular kernel (SK) non-linear fractional partial integro-differential equation (FPIDE). The spatial and temporal fractional derivatives are discretized by ExCuBS and the Caputo finite difference scheme, respectively. The present study found that it is stable and convergent. The validity of the current approach is examined on a few test problems, and the obtained outcomes are compared with those that have previously been reported in the literature.