Fractional Differential Equations and Expansions in Fractional Powers

Abstract

We use power series with rational exponents to find exact solutions to initial value problems for fractional differential equations. Certain problems that have been previously studied in the literature can be solved in a closed form, and approximate solutions are derived by constructing recursions for the relevant expansion coefficients.

Keywords

• Caputo fractional derivative
• fractional differential equations
• expansions in fractional powers
• fractional-order logistic equation