An Iterative Method Based on Fractional Derivatives for Solving Nonlinear Equations

The theory of fractional order derivatives are almost as old as the integer-order [5]. There are many applications, for example in physics [1], [2], [6], finance [8], [9] or biology [3]. Our aim is not to use fractional order operators to modeling such things, we only will use them as a device to prove a theoretical mathematical statement. In this work our goal is to find a solution numerically for the equation A(u) = f . If we assume that u is time-dependent, then one can do this by finding a stationary solution of the equation ¶tu(t)