The fractional equation of motion for fluid dynamics using Caputo's definition

Other Title(s)

معادلة الحركة الكسرية لديناميكا الموائع باستخدام تعريف كابوتو

Dissertant

al-Fuqaha, Rabiah Ahmad

Thesis advisor

Jaradat, Imad Khalid Yusuf

Comitee Members

al-Jarabah, Ala Abd Rabbih
al-Shar, Muhammad Abd al-Karim
al-Nawafilah, Khalid Isa

University

Mutah University

Faculty

Faculty of Science

Department

Department of physics

University Country

Jordan

Degree

Master

Degree Date

2016

English Abstract

In this work, the Lagrangian density was rewritten by using Caputo's fractional derivative, and from the fractional variational principle the fractional Euler-Lagrangian equation was obtained to find the equations of motion.

From the fractional Lagrangian density, the fractional Hamiltonian density was also obtained then we got the fractional Hamiltonian equations, and the energy-stress tensor was derived from the Noether's theorem in fractional form.

The Lagrangian densities was reformulated for fluid fields: single fluid, two mixture fluids, perfect fluid and ideal hydrodynamics in rotating frame, by using Caputo's fractional derivative, then from the fractional Euler-Lagrangian equation the equations that described the motion of fluid in fractional form were obtained .

After that, the Hamiltonian densities and the energy-stress tensors were obtained in fractional form from the fluid Lagrangian densities.

From these Hamiltonian densities the Hamiltonian equations of motion for the fluid in fractional form were also obtained.

The results in fractional form were compared with those in the classical form that were reached earlier, the classical equations were found to be special case from the fractional form.

Main Subjects

Physics

No. of Pages

73

Table of Contents

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Language

English

Data Type

Arab Theses

Record ID

BIM-749485