A finite-difference procedure to solve weakly singular integro partial differential equation with space-time fractional derivatives

Abstract

The main aim of the current paper is to propose an efficient numerical technique for solving space-time fractional partial weakly singular integro-differential equation. The temporal variable is based on the Riemann–Liouville fractional derivative and the spatial direction is based on the Riesz fractional derivative. Thus, to achieve a numerical technique, the time variable is discretized using a finite difference scheme with convergence order $${{\mathcal {O}}}(\tau ^{\frac{3}{2}})$$. Also, the space variable is discretized using a finite difference scheme with second-order accuracy. Furthermore, for the time-discrete and the full-discrete schemes error estimate has been presented to show the unconditional stability and convergence of the developed numerical method. Finally, two test problems have been illustrated to verify the efficiency, applicability and simplicity of the proposed technique.