Fractional integration and differentiation

2023/08/18 by Oleg Yaremko, Andrey Yachmenev, Yaremko, Oleg +1
Engineering · Mathematics · #34K07 (Secondary) #47G20 (Primary) #Advanced Control Systems Design #FOS: Mathematics #Fractional Differential Equations Solutions #G.1.2 #G.1.7 #General Mathematics (math.GM) #Iterative Methods for Nonlinear Equations

paper · pdf · doi:10.48550/arxiv.2309.03207

openalex publication_date 2023/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of functions and provides a series representation of integration. This representation will be useful for working with smooth functions and for approximation due to the potential reduction of the value of the sequential elements.

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