A novel fractional Bernoulli-Picard iteration method to solve fractional differential equations

This paper introduces a new computational method for solving linear and non-linear fractional differential equations (FDEs). Our method essentially consists of the combination of orthonormal Bernoulli polynomials  and the fractional form of the Picard iteration method. We name this method the fractional Bernoulli-Picard iteration method (FBPIM). Unlike the spectral method, the proposed method does not require solving a set of algebraic equations. We also discuss the convergence of the method. Moreover, some numerical examples are included and compared with previously published results to assess both the accuracy and suitability of the developed technique.

A novel fractional Bernoulli-Picard iteration method to solve fractional differential equations Keywords:

Caputo derivative , Picard iteration method , Orthonormal Bernoulli polynomials , Fractional differential equations , Numerical solution