Tarig Projected Differential Transform Method to Solve Fractional Nonlinear Partial Differential Equations

Recent advances in nonlinear analyzes and fractional calculus is to address the challenges arise in the solution methodology of nonlinear fractional partial differential equations. This paper presents a hybrid technique to solve nonlinear fractional partial differential equations, which is a combination of Tarig transform and Projected Differential Transform Method (TPDTM). The effectiveness of the method is examined by solving three numerical examples that arises in the field of heat transfer analyzes. In this proposed scheme the solution obtained as a convergent series and using the result the hyper diffusive process with pre local information regarding the heat transfer for different values of fractional order are analyzed. To validate the results and to analyze the computational efficiency of the proposed method a comparative study has been carried out with the solution obtained by the Laplace Adomian Decomposition Method (LADM) and Homotophy Pertubation Method (HPM) and observed good agreement. Also, the computational time in each method is calculated using CPU and the results are presented. It was observed that the proposed technique provide good results with less computational time than homotophy pertubation technique. Even though there is a uniformity between the solutions obtained by TPDTM and LADM, the proposed hybrid technique overcome the complexity of manupulation of Adomian polynomials in LADM and evaluation of integrals in hPM respectively. The methodology and the results presented in this paper clearly reveals the computational efficiency of the present method. The TPDTM, due to its computational efficiency has the potential to be used as a novel tool, not only for solving nonlinear fractional differential equations but also to analyse the prelocal information of the system.