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Generalizing of Finite Difference Method for Certain Fractional Order Parabolic PDE’s

Space-time fractional differential equation with integral term (S-TFDE) has been considered. 
The finite difference method (implicit and explicit) combined with the trapezoidal integration formula has been used to 
find special formula to solve this equation. The stability and convergence have been discussed. The effect of adding an 
integral term to the common classical equation has been considered.  Graphical representation of the calculate solutions 
(obtained by the explicit and the implicit methods) for three numerical examples with their exact solution, are 
considered. All the calculations and graphs are designed with the help of MATLAB.