Physical Sciences and Mathematics Commons^™

Studies On The Tempered Fractional Natural Decomposition Method, Nazek Ahmad Obeidat

Graduate College Dissertations and Theses

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, …