Ford, NevilleOsborne, Neil2022-03-092022-03-092021-07Osborne, N. (2021). Insights into the analysis of fractional delay differential equations [Unpublished doctoral thesis]. University of Chester.http://hdl.handle.net/10034/626737This thesis is concerned with determining the analytic solution, using the method of steps, of the following fractional delay differential equation initial interval problem (FDDE IIP), c Dαy(s) = −y(t − τ ) for t > 0, τ > 0, 0 < α < 1, and y ∈ A1(0, T ] 0 t y(t) = ϕ(t) for t ∈ (−τ, 0] The properties of the analytic solution obtained are a surprise but they do sit comfortably when compared with those of the analytic solutions of an ordinary differential equation initial value problem (ODE IVP), a delay differential equation initial interval problem (DDE IIP) and an fractional ordinary differential equation initial value problem (FODE IVP). Further the analytic solution formula obtained is closely related to that of the analytic solution formula of the DDE IIP. However, these insights into the analytic solution of the FDDE IIP we have not seen before, and differ from those published elsewhere.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/fractional delay differential equationinitial interval problemexistence and uniquenessanalytic solutioncontinuitysmoothnessThesis or dissertation2022-03-25Awaiting Board of Studies presentationThe full-text may be used and/or reproduced in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-profit purposes provided that: - A full bibliographic reference is made to the original source - A link is made to the metadata record in ChesterRep - The full-text is not changed in any way - The full-text must not be sold in any format or medium without the formal permission of the copyright holders. - For more information please email researchsupport.lis@chester.ac.uk