Further Studies on Ordinary Differential Equations Involving the M-Fractional Derivative

Khoshkenar, A.Ilie, M.Hosseini, K.Baleanu, D.Salahshour, S.Park, C.Lee, J. R.2024-03-282025-09-182024-03-282025-09-182022Khoshkenar, A. (2022). "Further studies on ordinary differential equations involving the M-fractional derivative", AIMS Mathematics, Vol.7, No.6, pp.10977-10993.2473-6988https://doi.org/10.3934/math.2022613https://hdl.handle.net/20.500.12416/11361Khoshkenar, Ali/0000-0002-4920-0316; Salahshour, Soheil/0000-0003-1390-3551In 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.eninfo:eu-repo/semantics/openAccessM-Fractional DerivativePower SeriesNew DefinitionsTheorems And CorollariesOrdinary Differential EquationsFurther Studies on Ordinary Differential Equations Involving the M-Fractional DerivativeFurther studies on ordinary differential equations involving the M-fractional derivativeArticle10.3934/math.20226132-s2.0-85128144975