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Title:	Fractional reduced differential transform method for solving fractional order differential equations
Authors:	Abu As'd Salah Abd Lateef (P84136)
Supervisor:	Ishak Hashim, Prof.
Keywords:	Fractional calculus Fractional differential equations Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia
Issue Date:	2020
Description:	The term fractional calculus is more than 300 year sold. It is a generalisation of the integer (classical) differentiation and integration to non-integer (arbitrary)order.Nowadays,fractional differential equations have gained much attention due to the tremendous use in fluid mechanics, mathematical biology, electrochemistry, physics, andsoon. Over the past decades, several analytical and approximate methods have been developed to solve nonlinear ordinary and partial fractional differential equations. Some of these methods are only generalisation from classic differentiation to fractional differentiation,while most of them remain opaque not only for scientists but also for mathematicians,and most solutions were given for special cases or a short time span. In this thesis a semi numerical-analytical method,called fractional reduced differential transform method for finding exact and aproximate solutions of linear fractional Helmholtz equation with appropriate initial conditions are first analysed. In most cases,we can write the solutions in compact forms and with the help of Mittag-Leffler function,we can find the exact or approximate solutions easily.Then,a fractional reduced differential transform method for finding approximate solutions of non-linear fractional Burgers�� equations is presented.This method is tested by solving three-dimensional fractional Burgers�� equations and a coupled system of fractional Burgers�� equations.This method needs only a small amount of computations and gives rapid convergence to the exact solutions since only few iterations are enough to yield good accuracy with exact solutions. Furthermore,a new modification of fractional reduced differential transform method to find exact and approximate solutions for non homogeneous linear multi-termtime-fractional diffusion equations of constant coefficients in a bounded domain is presented.Different applications in two and three fractional-order terms are given to illustrate the new modification method.The results show that thi smodification is apowerful method since it can solve one of the unfamiliar types of fractional differential equations and can be generalised to other types of multi-term time-fractional equations.Lastly,a fractional multi-step differential transformed method is applied to the so-called fractional SIS epidemic model with imperfect vaccination.This model is robust and precise which can give new interpretations for various types of dynamical systems.,Ph.D
Pages:	144
Call Number:	QA372.A238 2020 tesis
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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