A difference scheme based on cubic B-spline quasi-interpolation for the solution of a fourth-order time-fractional partial integro-differential equation with a weakly singular kernel

This paper presents a difference scheme by considering cubic B-spline quasi-interpolation for the numerical solution of a fourth-order time-fractional integro-differential equation with a weakly singular kernel. The fractional derivative of the mentioned equation has been described in the Caputo sense. Time fractional derivative is approximated by a scheme of order O ( τ 2 - α ) and the Riemann–Liouville fractional integral term is discretized by the fractional trapezoidal formula. The spatial second derivative has been approximated using the second derivative of the cubic B-spline quasi-interpolation. The discrete scheme leads to the solution of a system of linear equations. We show that the proposed scheme is stable and convergent. In addition, we have shown that the order of convergence is O ( τ 2 - α + h 2 ) . Finally, various numerical examples are presented to support the fruitfulness and validity of the numerical scheme.