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.2024-03-282024-03-282022Khoshkenar, A. (2022). "Further studies on ordinary differential equations involving the M-fractional derivative", AIMS Mathematics, Vol.7, No.6, pp.10977-10993.24736988http://hdl.handle.net/20.500.12416/7798In 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 DerivativeNew DefinitionsTheorems And CorollariesOrdinary Differential EquationsPower SeriesFurther studies on ordinary differential equations involving the M-fractional derivativeFurther Studies on Ordinary Differential Equations Involving the M-Fractional DerivativeArticle76109771099310.3934/math.2022613