Precise interpretation of the conformable fractional derivative

2018/05/07 by Ahmed A. Abdelhakim, Abdelhakim, Ahmed A.
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical and Theoretical Analysis #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1805.02309

openalex publication_date 2018/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let α∈ ]0,1[. We prove that the existence of the conformable fractional derivative T_αf of a function f:[0,∞[ \longrightarrow ℝ introduced by Khalil et al. in [R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014) 65-70] is equivalent to classical differentiability. Precisely the fractional α-derivative of f is the pointwise product T_αf(x)=x^1-αf^′(x), x>0. This simplifies the recent results concerning conformable fractional calculus.

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