Generalized fractional power series solutions for fractional differential equations

Abstract

The extension of fractional power series solutions for linear fractional differential equations with variable coefficients is considered. Generalized series expansions involving integer powers and fractional powers in the independent variable have recently been shown to provide solutions to certain linear fractional order differential equations. In these studies the generalized series could be formulated as the Cauchy product of a standard power series with integer powers and a fractional power series with powers as multiples of a fractional exponent. Here we show that generalized fractional powers series can provide solutions to a wider class of problems if there is no requirement that the series can be formulated as a Cauchy product.