An Efficient Numerical Method for Fractional Advection–Diffusion–Reaction Problem with RLC Fractional Derivative.

In this paper, we consider a two-point boundary-value problem with a Riemann–Liouville–Caputo fractional derivative of order α ∈ (1 , 2) . We solve this boundary-value problem in a sequence of processes, first using the shooting technique based on the secant iterative method, we convert the boundary-value problem into an initial-value problem, then the initial-value problem is transformed into an equivalent Volterra integral equation with weakly singular kernel. Finally, we find the approximate solution of the resultant equation by using a discretization scheme on a uniform mesh. The method's convergence analysis has been thoroughly established, and it demonstrates that the scheme is first-order convergent. To show the effectiveness of the suggested approach, numerical results are provided. [ABSTRACT FROM AUTHOR]