Fractional Differential Equations and Expansions in Fractional Powers

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.

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In this paper, we utilize power series with rational exponents to obtain exact solutions for initial value problems of fractional differential equations. By constructing recursions for expansion coefficients, certain problems previously studied in the literature can be solved analytically and approximate solutions can be derived.