Submitting Campus
Daytona Beach
Department
Mathematics
Document Type
Article
Publication/Presentation Date
12-19-2018
Abstract/Description
A new type of ordinary differential equation is introduced and discussed: time-dependent order ordinary differential equations. These equations are solved via fractional calculus by transforming them into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equation represent deformations of the solutions of the classical (integer order) differential equations, mapping them into one-another as limiting cases. This equation can also move, remove or generate singularities without involving variable coefficients. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers is observed.
Publication Title
Symmetry
DOI
https://doi.org/10.3390/sym10120771
Publisher
MDPI AG
Grant or Award Name
Natural Science Foundation of China Grant Nos. NSFC-51639003 and NSFC-51679037, National Key Research and Development Program of China (Grant Nos. 2019 YFC0312400 and 2017 YFE0132000), the National Natural Science Foundation of China (Grant Nos. 51975032 and 51939003), and the State Key Laboratory of Structural Analysis for Industrial Equipment (Grant No. S18408)
Scholarly Commons Citation
Ludu, A. (2018). Nonlocal Symmetries for Time-Dependent Order Differential Equations. Symmetry, 10(12). https://doi.org/10.3390/sym10120771
