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.

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}}}^{...

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Bibliographic Details

Main Authors:	R. Marcinkevicius, I. Telksniene, T. Telksnys, Z. Navickas, M. Ragulskis
Format:	Article
Language:	English
Published:	AIMS Press 2022-07-01
Series:	AIMS Mathematics
Subjects:	fractional differential equation operator calculus fractional power series expansion
Online Access:	https://www.aimspress.com/article/doi/10.3934/math.2022905?viewType=HTML