ANALYTIC STUDY ON TIME- FRACTIONAL THIRD ORDER PARTIAL DIFFERENTIAL EQUATIONS OF ONE AND TWO DIMENSIONS

Abstract

The main contribution of this study is to explore an analytical framework for solving time-fractional third-order PDEs in one and two dimensions using Laplace Adomain decomposition Method (LADM) and q-Homotopy Analysis Transform Method (q-HATM).To define fractional derivative, the Caputo operator is used for both fractional and integer orders.The solutions are obtained in the form of series.To understand the procedure two theorems for each method and two numerical examples with their graphical solutions for different values of α,(0 < α ≤ 1) are taken. These results validate the effectiveness of fractional order PDEs in modeling complex physical and engineering phenomena, such as heat conduction, viscoelasticity, and transport processes in heterogeneous media.