期刊
AIMS MATHEMATICS
卷 7, 期 6, 页码 10977-10993出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2022613
关键词
M-fractional derivative; power series; new definitions; theorems and corollaries; ordinary differential equations
In this paper, a power series based on the M-fractional derivative is introduced, and new definitions, theorems, and corollaries regarding the power series in the M sense are presented and formally proved. Several ordinary differential equations involving the M-fractional derivative are solved to examine the validity of the results presented in the study.
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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