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.