Fractional Newton–Raphson Method Accelerated with Aitken’s Method

In the following paper, we present a way to accelerate speed of convergence fractional Newton–Raphson (F N–R) method, which seems have an order at least linearly for case in α derivative is different from one. A simplified constructing Riemann–Liouville (R–L) operators, integral and presented along with examples its application on functions. Furthermore, introduction Aitken’s method made it explained why has ability iterative methods, finally results that were obtained when implementing F N–R where shown converges faster than simple N–R.