Open AccessFurther studies on ordinary differential equations involving the $ M $-fractional derivative
Author(s) -
A. Khoshkenar,
Mousa Ilie,
K. Hosseini,
Dumitru Băleanu,
Soheil Salahshour,
C. Park,
J. R. Lee
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2022613
Subject(s) - fractional calculus , mathematics , differentiable function , ode , derivative (finance) , ordinary differential equation , power series , series (stratigraphy) , taylor series , generalizations of the derivative , order (exchange) , mathematical analysis , differential equation , paleontology , finance , financial economics , economics , biology
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.