Q-Homotopy Analysis Aboodh Transform Method based solution of proportional delay time-fractional partial differential equations

Abstract

In this manuscript, a hybrid method namely q-Homotopy Analysis Aboodh Transform Method (q-HAATM) has been applied for obtaining the solutions of fractional partial differential equations (PDEs) with proportional delay (PD) described in the Caputo sense. q-HAATM is the amalgamation of the Homotopy Analysis Method (HAM) and Aboodh Transform Method (ATM). Three example problems are solved, and the results are obtained in series form. It is noticed from the obtained results that the present method is easy to apply and provides a proper way of choosing parameters ħ and n which give a better approximate solution.

Subject Classification: (2010):

• 65H20
• 60H15
• 35R11

Keywords:

• Caputo fractional derivative
• Homotopy Analysis Method
• Transform Method
• proportional delay PDEs