變導(dǎo)數(shù)分?jǐn)?shù)階Pfaff-birkhoff變分問題及其對稱性研究.pdf

1、本文在Riemann-Liouville型、Caputo型和Riesz型變導(dǎo)數(shù)分?jǐn)?shù)階模型下，研究變導(dǎo)數(shù)分?jǐn)?shù)階Birkhoff系統(tǒng)和變導(dǎo)數(shù)分?jǐn)?shù)階廣義Birkhoff系統(tǒng)的Noether對稱性與守恒量.建立三種模型下的變導(dǎo)數(shù)分?jǐn)?shù)階Pfaff-Birkhoff原理和變導(dǎo)數(shù)分?jǐn)?shù)階廣義Pfaff-Birkhoff原理，由此導(dǎo)出相應(yīng)的變導(dǎo)數(shù)分?jǐn)?shù)階Birkhoff方程與變導(dǎo)數(shù)分?jǐn)?shù)階廣義Birkhoff方程.進(jìn)一步，建立變導(dǎo)數(shù)分?jǐn)?shù)階Birkhoff系統(tǒng)

2、與變導(dǎo)數(shù)分?jǐn)?shù)階廣義Birkhoff系統(tǒng)的Noether定理.
　　第一部分，基于Riemann-Liouville型變導(dǎo)數(shù)分?jǐn)?shù)階導(dǎo)數(shù)，建立變導(dǎo)數(shù)分?jǐn)?shù)階Pfaff-Birkhoff原理，并導(dǎo)出Riemann-Liouville型變導(dǎo)數(shù)分?jǐn)?shù)階Birkhoff方程.研究變導(dǎo)數(shù)分?jǐn)?shù)階Pfaff-Birkhoff變分問題，建立變導(dǎo)數(shù)分?jǐn)?shù)階Birkhoff系統(tǒng)的Noether定理.其次，研究Riemann-Liouville型變導(dǎo)數(shù)分?jǐn)?shù)階廣義

3、Pfaff-Birkhoff原理，給出Riemann-Liouville型變導(dǎo)數(shù)分?jǐn)?shù)階廣義Birkhoff方程，進(jìn)一步建立Riemann-Liouville型變導(dǎo)數(shù)分?jǐn)?shù)階廣義Birkhoff系統(tǒng)的Noether定理.
　　第二部分，基于Caputo型變導(dǎo)數(shù)分?jǐn)?shù)階導(dǎo)數(shù)，建立變導(dǎo)數(shù)分?jǐn)?shù)階Pfaff-Birkhoff原理，并導(dǎo)出Caputo型變導(dǎo)數(shù)分?jǐn)?shù)階Birkhoff方程.研究變導(dǎo)數(shù)分?jǐn)?shù)階Pfaff-Birkhoff分問題，建立變導(dǎo)數(shù)

4、分?jǐn)?shù)階Birkhoff系統(tǒng)的Noether定理.其次，研究Caputo型變導(dǎo)數(shù)分?jǐn)?shù)階廣義Pfaff-Birkhoff原理，給出Caputo型變導(dǎo)數(shù)分?jǐn)?shù)階廣義Birkhoff方程，進(jìn)一步建立Caputo型變導(dǎo)數(shù)分?jǐn)?shù)階廣義Birkhoff系統(tǒng)的Noether定理.
　　第三部分，基于Riesz-Riemann-Liouville型變導(dǎo)數(shù)分?jǐn)?shù)階導(dǎo)數(shù)與Riesz-Caputo型變導(dǎo)數(shù)分?jǐn)?shù)階導(dǎo)數(shù)，建立相應(yīng)的變導(dǎo)數(shù)分?jǐn)?shù)階Pfaff-Birkh

5、off原理，并導(dǎo)出Riesz-Riemann-Liouville型和Riesz-Caputo型變導(dǎo)數(shù)分?jǐn)?shù)階Birkhoff方程.研究變導(dǎo)數(shù)分?jǐn)?shù)階Pfaff-Birkhof變分問題，建立變導(dǎo)數(shù)分?jǐn)?shù)階Birkhoff系統(tǒng)的Noether定理.其次，研究了Riesz-Riemann-Liouville型變導(dǎo)數(shù)分?jǐn)?shù)階廣義Pfaff-Birkhoff原理與Riesz-Caputo型變導(dǎo)數(shù)分?jǐn)?shù)階廣義Pfaff-Birkhoff原理，給出相應(yīng)的變導(dǎo)數(shù)