Numerical Analysis of Fractional-Order Parabolic Equation Involving Atangana–Baleanu Derivative

Abstract

In this study, the suggested q-homotopy analysis transform method is used to compute a numerical solution of a fractional parabolic equation, and the solution is obtained in a fast convergent series. The leverage and efficacy of the suggested technique are demonstrated by the test examples provided. The results that were acquired are graphically displayed. The series solution in a sizable admissible domain is handled in an extreme way by the current method. It provides us with a simple means of modifying the solution’s convergence zone. The effectiveness and potential of the suggested algorithm are explicitly shown in the results using graphs.

Keywords

• fractional parabolic equations
• q-homotopy analysis transform method
• Aboodh transform
• Atangana–Baleanu operator