Numerical Solutions for the Nonlinear PDEs of Fractional Order by Using a New Double Integral Transform with Variational Iteration Method

Abstract

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

Keywords

• Double Sumudu-Elzaki transform, Fractional Calculus, Fractional nonlinear PDEs, Numerical Solution, Variational Iteration Method.