Derivative-Free Conformable Iterative Methods for Solving Nonlinear Equations

The iterative solving nonlinear algebraic or transcendental equations by use of conformable derivative approximations. For the purpose of solving nonlinear equations, we modify the approximation of conformable derivatives and build iterative schemes (such as Secant-type techniques and Steffensen-type schemes) that do not need conformable derivatives. Our sources tell us that the Secant conformable scheme and the Steffensen conformable technique are the first two optimum conformable derivative-free schemes. The Secant scheme is a memory process. All the while maintaining the classical case order, a convergence analysis is performed, and numerical performance is verified to verify that the theoretical findings are valid. Utilizing these techniques in tandem with extensive datasets of convergent initial estimates has the potential to provide numerical benefits compared to more traditional approaches. Conformable calculus offers an alternative to fractional calculus, which does not evaluate particular functions like Gamma or Mittag-Leffler functions, and has a minimal processing cost. We now look at the schemes presented in this book and how they rely on the initial estimations, particularly with regard to the convergence planes.