Series Approximate Analytical Solution of Fractional Partial Differential Equations

The primary objective of this thesis work is the presentation of a new iterative procedure to achieve both series approximate solution and analytical solution of positive non-integer order partial differential equations. The order of the derivative is considered according to Caputo’s assumption. This iterative procedure is called Aboodh transform iterative method. The Aboodh transform iterative method is a combination of the new iterative method with the Aboodh transform. The new iterative method was introduce as important tool to linearize all the associated nonlinear terms since the Aboodh transform cannot handle the nonlinear terms. Several examples and cases are examined. The solutions obtained were compared with solutions obtained by other existing methods in literature. Also, the solutions reveals that the Aboodh transform iterative procedure is less computational involving and requires no restrictive assumption, Lagrange multipliers and Adomian polynomial. The software used to implement the Aboodh transform iterative procedure are LaTex, MATHEMATICA 10.0 and MATLAB R2021.