Preprint Article Version 1 This version is not peer-reviewed

Nonlocal Symmetries for Time-Dependent Order Differential Equations

Version 1 : Received: 5 November 2018 / Approved: 7 November 2018 / Online: 7 November 2018 (09:15:19 CET)

A peer-reviewed article of this Preprint also exists.

Ludu, A. Nonlocal Symmetries for Time-Dependent Order Differential Equations. Symmetry 2018, 10, 771. Ludu, A. Nonlocal Symmetries for Time-Dependent Order Differential Equations. Symmetry 2018, 10, 771.

Journal reference: Symmetry 2018, 10, 771
DOI: 10.3390/sym10120771

Abstract

A new type of ordinary differential equation is introduced and discussed, namely, the time-dependent order ordinary differential equations. These equations can be solved via fractional calculus and are mapped into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equations smoothly deforms solutions of the classical integer order ordinary differential equations into one-another, and can generate or remove singularities. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers was also proved.

Subject Areas

time-dependent order of differentiation; fractional calculus;fractional derivative;differential equations;complex systems;Volterra integral equation;VODE;DODE;dynamical evolution

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