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.
Citation: R. Marcinkevicius, I. Telksniene, T. Telksnys, Z. Navickas, M. Ragulskis. 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[J]. AIMS Mathematics, 2022, 7(9): 16536-16554. doi: 10.3934/math.2022905
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.
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