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On Fractional Differential Equations...

Li, Yulong.

On Fractional Differential Equations and Related Questions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	On Fractional Differential Equations and Related Questions.
Author:	Li, Yulong.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2019
Description:	95 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
Notes:	Advisor: Ginting, Victor.
Contained By:	Dissertations Abstracts International81-02B.
Subject:	Mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13880082
ISBN:	9781085630009

On Fractional Differential Equations and Related Questions.
Li, Yulong.

On Fractional Differential Equations and Related Questions. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 95 p.

Source: Dissertations Abstracts International, Volume: 81-02, Section: B.

Thesis (Ph.D.)--University of Wyoming, 2019.

This item must not be sold to any third party vendors.

The study of fractional calculus theory has attracted the attention of many of the world’s applied mathematicians during the past decades, mainly because of the popular application of various fractional-order differential equations in modeling challenging physical phenomena including anomalous diffusion that is present in microscopic and macroscopic scales. Compared to integer-order differential equations, the study of fractional-order differential equations becomes more subtle and sophisticated to deal with due to appearance of non-local operators. To date, this subject remains a dynamic field of inquiry, with many interesting open questions. This dissertation collects results of several aspects of fractional-order differential equations and related questions. More precisely, it includes three topics: 1) analysis of fractional order differential equations; 2) investigation of fractional Sobolev spaces from the perspective of Riemann-Liouville operators; 3) study of harmonic analysis from the perspective of Riemann-Liouville operators. The first topic is focused on fractional diffusion-advection-reaction equation and the striking structure of the true solution, which gives a glimpse of some common features shared by general fractional-order differential equations. Existence, uniqueness and regularity of solution will be established. In the second and third topic, it will be shown how fractional Riemann-Liouville operators naturally arisefrom the subject of fractional Sobolev spaces and harmonic analysis, with an illustration on how Riemann-Liouville operators, fractional Sobolev spaces and analog filters are tangled together.

ISBN: 9781085630009Subjects--Topical Terms:

184409
Mathematics.

On Fractional Differential Equations and Related Questions.
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500 $a Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
500 $a Advisor: Ginting, Victor.
502 $a Thesis (Ph.D.)--University of Wyoming, 2019.
506 $a This item must not be sold to any third party vendors.
506 $a This item must not be added to any third party search indexes.
520 $a The study of fractional calculus theory has attracted the attention of many of the world’s applied mathematicians during the past decades, mainly because of the popular application of various fractional-order differential equations in modeling challenging physical phenomena including anomalous diffusion that is present in microscopic and macroscopic scales. Compared to integer-order differential equations, the study of fractional-order differential equations becomes more subtle and sophisticated to deal with due to appearance of non-local operators. To date, this subject remains a dynamic field of inquiry, with many interesting open questions. This dissertation collects results of several aspects of fractional-order differential equations and related questions. More precisely, it includes three topics: 1) analysis of fractional order differential equations; 2) investigation of fractional Sobolev spaces from the perspective of Riemann-Liouville operators; 3) study of harmonic analysis from the perspective of Riemann-Liouville operators. The first topic is focused on fractional diffusion-advection-reaction equation and the striking structure of the true solution, which gives a glimpse of some common features shared by general fractional-order differential equations. Existence, uniqueness and regularity of solution will be established. In the second and third topic, it will be shown how fractional Riemann-Liouville operators naturally arisefrom the subject of fractional Sobolev spaces and harmonic analysis, with an illustration on how Riemann-Liouville operators, fractional Sobolev spaces and analog filters are tangled together.
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