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

http://dx.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)

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