2022/04/26 by Leila Gholizadeh Zivlaei, Zivlaei, Leila Gholizadeh, Angelo B. Mingarelli +1
Mathematics · #26A33 #34A08 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Iterative Methods for Nonlinear Equations #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2204.12450
openalex publication_date 2022/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We continue the development of the basic theory of generalized derivatives as introduced in \citeJPA and give some of their applications. In particular, we formulate versions of a weak maximum principle, Rolle's theorem, the Mean value theorem, the Fundamental theorem of Calculus, Integration by parts, along with an existence and uniqueness theorem for a generalized Riccati equation, each of which includes, as corollaries, the corresponding version for conformable fractional derivatives considered by \citekat, \citekha among many others. Finally, we show that for each α> 1 there is a fractional derivative and a corresponding function whose fractional derivative fails to exist everywhere on the real line.