High-order fractional linear differential equations do not describe stochastic processes with finite state space

The replacement of the classical derivative in the governing equation of a continuous-time Markov process with finite state space by a fractional derivative of arbitrary order $α>1$ produces solutions that are mathematically incompatible with the theory of stochastic processes.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-02
DOI
https://doi.org/10.48550/arxiv.2611.02954
Primary Topic
Fractional Differential Equations Solutions
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

High-order fractional linear differential equations do not describe stochastic processes with finite state space

P. Van Mieghem
arXiv (Cornell University)
Fractional Differential Equations Solutions
preprint

High-order fractional linear differential equations do not describe stochastic processes with finite state space

P. Van Mieghem
preprint en

Abstract

The replacement of the classical derivative in the governing equation of a continuous-time Markov process with finite state space by a fractional derivative of arbitrary order $α>1$ produces solutions that are mathematically incompatible with the theory of stochastic processes.

arXiv (Cornell University)
Fractional Differential Equations Solutions
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon
High-order fractional linear differential equations do not describe stochastic processes with finite state space — P. Van Mieghem · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS