Work

The Fractional-Order Effect Induced by Space–Time Order Mismatch in Operator Differential Equations

Year: 2025

Type: article

Abstract: This paper reports an interesting phenomenon in which fractional-order effects can be induced by the mismatch of the differential orders of space and time; that is, fractional-order effects can be induced by space–time symmetry breakage. Classical mathematical equations can be transformed into differential equations of undetermined operators. We confirmed that the presence of fractional-order operator solutions in operator differential equations is contingent upon the mismatch of differential orders of space and time, which can induce both fractional operators in the time domain and fractional operators in the space domain. The introduction of symmetry breakage and operators of space and time offers novel insights into understanding nonlocal phenomena within the space–time continuum.

Source: Symmetry

DOI: 10.3390/sym17050762

Authors: Yajun Yin, Tianyi Zhou, Ruiheng Jiang, Xiaobin Yu, Chaoqian Luo

Institutions: Tsinghua University, Beihang University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: National Natural Science Foundation of China