Further studies on ordinary differential equations involving the M-fractional derivativeopen access
- Authors
- Khoshkenar, Amin.; Ilie, Mousa; Hosseini, Kaave; Baleanu, Dumitru; Salahshour, Soheil; Park, Choon kil; Lee, Jung-Rye
- Issue Date
- Apr-2022
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Keywords
- M-fractional derivative; power series; new definitions; theorems and corollaries; ordinary differential equations
- Citation
- AIMS MATHEMATICS, v.7, no.6, pp.10977 - 10993
- Indexed
- SCIE
SCOPUS
- Journal Title
- AIMS MATHEMATICS
- Volume
- 7
- Number
- 6
- Start Page
- 10977
- End Page
- 10993
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/138963
- DOI
- 10.3934/math.2022613
- Abstract
- In the current paper, the power series based on the M-fractional derivative is formally introduced. More peciesely, the Taylor and Maclaurin expansions are generalized for fractional-order differentiable functions in accordance with the M-fractional derivative. Some new definitions, theorems, and corollaries regarding the power series in the M sense are presented and formally proved. Several ordinary differential equations (ODEs) involving the M-fractional derivative are solved to examine the validity of the results presented in the current study.
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