A New Method For Solving Fractional And Classical Differential Equations Based On a New Generalized Fractional Power Series

The main objective of this paper is to introduce an algorithm for solving fractional and classical differential equations based on a new generalized fractional power series. The algorithm relies on expanding the solution of an FDE or an ODE as a generalized power series, shedding light on the choice of the exponent for the monomials. Furthermore, it accommodates situations where terms in the equation are multiplied by tαfor example. The key contribution is how the exponents for these terms are chosen, which is different from traditional methods.