Discrete fractional Calculus and Inequalities

2009/11/17 by George A. Anastassiou, Anastassiou, George A.
Decision Sciences · Engineering · Mathematics · #26A33 #34A25 #39A12 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Numerical methods in engineering #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.0911.3370

openalex publication_date 2009/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here we define a Caputo like discrete fractional difference and we compare it to the earlier defined Riemann-Liouville fractional discrete analog. Then we produce discrete fractional Taylor formulae for the first time, and we estimate their remainders. Finally, we derive related discrete fractional Ostrowski, Poincare and Sobolev type inequalities.

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