Ask a Librarian

Threre are lots of ways to contact a librarian. Choose what works best for you.

HOURS TODAY

10:00 am - 3:00 pm

Reference Desk - Virtual

CONTACT US BY PHONE

(802) 656-2022

Voice

(802) 503-1703

Text

MAKE AN APPOINTMENT OR EMAIL A QUESTION

Schedule an Appointment

Meet with a librarian or subject specialist for in-depth help.

Email a Librarian

Submit a question for reply by e-mail.

WANT TO TALK TO SOMEONE RIGHT AWAY?

Library Hours for Wednesday, August 17th

All of the hours for today can be found below. We look forward to seeing you in the library.
HOURS TODAY
8:00 am - 4:30 pm
MAIN LIBRARY

SEE ALL LIBRARY HOURS
WITHIN HOWE LIBRARY

MapsClosed

Media ServicesTBD

Reference Desk10:00 am - 3:00 pm

OTHER DEPARTMENTS

Special Collections10:00 am - 5:00 pm

Dana Medical Library7:30 am - 11:00 pm

 

CATQuest

Search the UVM Libraries' collections

UVM Theses and Dissertations

Browse by Department
Format:
Online
Author:
Obeidat, Nazek Ahmad
Dept./Program:
Mathematics
Year:
2022
Degree:
Ph. D.
Abstract:
In Fractional Calculus (FC), the notion of fractional derivatives and integrals arise from convolutions with a power law, which, when multiplied by an exponential factor, one obtains tempered fractional derivatives and integrals. The purpose of this dissertation is to develop theories and applications of a new technique in FC called the Tempered Fractional Natural Transform Method (TFNTM). This method can be used to solve a myriad of problems in linear and nonlinear ordinary and partial differential equations. We present convergence analysis, give error estimates, and provide exact solutions, with graphical illustrations, to many well-known problems in tempered fractional differential equation, such as the time-space tempered fractional convection-diffusion equation (FCDE) and tempered fractional Black-Scholes equation (FBSE) arising in the financial market. To further show the accuracy and efficiency of our approach, we also apply our methodology to a nonlinear time-fractional biological population model for the dispersal of animals within an enclave. Indeed, finding exact solutions to tempered fractional differential equations (TFDEs) is far from trivial. The proposed methodology, which has wide applications in science and engineering fields, is an excellent addition to the myriad of techniques for solving TFDE problems, and an alternate method with considerable promise for further practical applications.
Note:
Access to this item embargoed until 04/13/2023.