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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.
- Source :
- AIMS Mathematics, Vol 7, Iss 9, Pp 16536-16554 (2022)
- Publication Year :
- 2022
- Publisher :
- AIMS Press, 2022.
-
Abstract
- 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.
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 7
- Issue :
- 9
- Database :
- Directory of Open Access Journals
- Journal :
- AIMS Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.997a35dd67b44b9be22029a095ea9b8
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/math.2022905?viewType=HTML