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-Reference-Cited by-同舟云学术

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

Published:2022 Issue:9 Volume:7 Page:16536-16554
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Marcinkevicius R.¹,Telksniene I.²,Telksnys T.²,Navickas Z.²,Ragulskis M.²

Affiliation:

1. Department of Software Engineering, Kaunas University of Technology, Studentu 50-415, Kaunas LT-51368, Lithuania

2. Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania

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>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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