Mathematical analysis of fractional-order convection-reaction-diffusion equations under Caputo fractional derivative

Mashael M AlBaidani^*

• Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia

The main objective of this study is to employ two unique methods to approximately solve the time-fractional convection-reaction-diffusion equations (CRDEs). The suggested techniques combine the ado-mian decomposition approach, the homotopy perturbation method, and the Yang transform. He's poly-nomials and adomian polynomials are employed to address the nonlinearity that develops in our assumed problems. To clarify the efficacy of the employed schemes, three test examples are taken into account. This paper considers sophisticated approaches and the fractional operator in this aspect to obtain satisfactory approximations to the provided problems. We first build the Yang transforms of the Caputo fractional derivative and apply them for CRDEs to obtain improved approximations after a finite number of iterations. The two suggested methods are used to generate some extremely accurate analytical ap-proximations. The approximations obtained through these methods are represented as convergent series solutions. It has been observed that the solution obtained using the suggested methods converges at the desired rate to the precise solution. To show the usefulness of the offered techniques, we provide some graphical representations of the precise and analytical results, which are in excellent agreement with one another. In addition, we used a number of tables for different fractional orders to visually represent the physical behavior of the approximate solution. The convergence of the fractional solutions towards integer order solutions is examined for the efficacy of the current strategies. The proposed methods are validated by solving four important cases. The suggested solutions are proven to be very effective, straightforward, and appropriate for other nonlinear issues raised in science and engineering.