Research Information System
Journal of Mathematics, vol.2022, 2022 (SCI-Expanded)
.The current manuscript is concerned with the development of the Newton-Raphson method, playing a significant role in mathematics and various other disciplines such as optimization, by using fractional derivatives and fractional Taylor series expansion. The development and modification of the Newton-Raphson method allow us to establish two new methods, which are called first- and second-order fractional Newton-Raphson (FNR) methods. We provide convergence analysis of first- and second-order fractional methods and give a general condition for the convergence of higher-order FNR. Finally, some illustrative examples are considered to confirm the accuracy and effectiveness of both methods.