AN ANALYTICAL AND APPROXIMATE SOLUTION FOR LINEAR VOLTERRA PARTIAL INTEGRO-DIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL USING THE FRACTIONAL DIFFERENTIAL TRANSFORM METHOD

In this paper, an analytical approximate method is proposedfor solving linear Volterra partial integro-differential equations with a weaklysingular kernel. This method is based on the fractional differential trans-form method (FDTM). The approximate solutions of these equations arecalculated in the form of a nite series with easily computable terms. wepropose (FDTM) for equation typically arises in viscoelasticity. The an-alytic solution is represented by an in nite series. The existence theoremfor differential transform with the weak kernel of an integral equation onone dimension was provided by E.Rahimi,et al. In this paper, it will beextended on two dimensional FDTM.

AN ANALYTICAL AND APPROXIMATE SOLUTION FOR LINEAR VOLTERRA PARTIAL INTEGRO-DIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL USING THE FRACTIONAL DIFFERENTIAL TRANSFORM METHOD Keywords:

Weakly singular kernel , fractional differential transform method (FDTM) , Volterra partial integro-differential equations , viscoelasticity