The construction of solutions to $ {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)} $ type FDEs via reduction to $ \left({}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)}\right)^n $ type FDEs

Abstract

<abstract><p>A scheme for the integration of $ \, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)} $-type fractional differential equations (FDEs) is presented in this paper. The approach is based on the expansion of solutions to FDEs via fractional power series. It is proven that $ \, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)} $-type FDEs can be transformed into equivalent $ \left(\, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)}\right)^n $-type FDEs via operator calculus techniques. The efficacy of the scheme is demonstrated by integrating the fractional Riccati differential equation.</p></abstract>