Higher order graded mesh scheme for time fractional differential equations

In this article, we propose a (3 - alpha ) th, alpha is an element of (0,1) order approximation to Caputo fractional (C-F) derivative using graded mesh and standard central difference approximation for space derivatives, to obtain the approximate solution of time fractional partial differential equations (TFPDE). The proposed approximation for the C-F derivative tackles the singularity at origin effectively and is easily applicable to diverse problems. The stability analysis and truncation error bounds of the proposed scheme are discussed, and along with this, the required regularity of the solution is analysed. Numerous and varied examples are presented to support the theory.