Application of Modified Laplace Variational Iteration Hybrid Approach for Solving Time-Fractional Fourth-Order Parabolic PDEs

The current study is aimed at obtaining analytical solutions of fourth-order parabolic partial differential equations of time-fractional derivative with variable coefficients. The modified Laplace variational iteration approach and the homotopy perturbation method were used to treat nonlinear, fourth-order, time-fractional partial differential equations with time-fractional derivatives. This approach is essential for specifying the Lagrange multiplier without applying integration or convolution methods via recurrence relations. Ultimately, we observed that the method employed for tackling fractional-order partial differential equations is more precise, simple, and computationally efficient. Three significant illustrative instances are solved to validate the suggested approach. In summary, various fractional-order partial differential equations can be solved using the current method, which is a simple and precise analytical approach.