Analysis of the Fractional Integrodifferentiability of Power Functions and some Identities with Hypergeometric Functions

2016/12/21 by Fabio G. Rodrigues, Fabio Grangeiro Rodrigues, Rodrigues, Fabio Grangeiro +3
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #math.CA

paper · pdf · doi:10.48550/arxiv.1612.07240

22 pages. This new version has a correction on Eq.(16) - (18), which had some minor misprints in the previous version

openalex publication_date 2016/12/21 · arxiv created 2018/11/29 · arxiv updated 2018/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we show that it is possible to calculate the fractional integrals and derivatives of order α (using the Riemann-Liouville formulation) of power functions ( t-∗) ^β with β being any real value, so long as one pays attention to the proper choosing of the lower and upper limits according to the original function's domain. We, therefore, obtain valid expressions that are described in terms of function series of the type ( t-∗) ^±α+k and we also show that they are related to the famous hypergeometric functions of the Mathematical-Physics.

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