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Bagley-Torvik型分数阶微分方程和包含非局部积分边值问题
引用本文:陈丽珍,Badawi Hamza Eibadawi IBRAHIM,李刚.Bagley-Torvik型分数阶微分方程和包含非局部积分边值问题[J].数学研究及应用,2019,39(4):383-394.
作者姓名:陈丽珍  Badawi Hamza Eibadawi IBRAHIM  李刚
作者单位:山西财经大学应用数学学院, 山西 太原 030006,扬州大学数学科学学院, 江苏 扬州 225002,扬州大学数学科学学院, 江苏 扬州 225002
基金项目:国家自然科学基金(Grant Nos.11571300; 11871064).
摘    要:In this article,we consider the Bagley-Torvik type fractional differential equation ~cD~(ν1) l(t)-a~cD~(ν2) l(t) = g(t, l(t)) and differential inclusion ~cD~(ν1) l(t)-a~cD~(ν2) l(t) ∈ G(t, l(t)),t ∈(0, 1) subjecting to l(0) = l_0,and■ ds where 1 ν_1 ≤ 2, 1 ≤ν_2 ν_1,0 ω≤ 1, χ = ν_1-ν_2 0, a, λ′are given constants. By using Leray-Schauder degree theory and fixed point theorems, we prove the existence of solutions. Our results extend the existence theorems for the classical Bagley-Torvik equation and some related models.

关 键 词:分数阶微分方程和包含    积分边值问题    Leray-Schauder度理论
收稿时间:2018/6/2 0:00:00
修稿时间:2019/4/11 0:00:00

Nonlocal Integral Boundary Value Problem of Bagley-Torvik Type Fractional Differential Equations\\ and Inclusions
Lizhen CHEN,Badawi Hamza Eibadawi IBRAHIM and Gang LI.Nonlocal Integral Boundary Value Problem of Bagley-Torvik Type Fractional Differential Equations\\ and Inclusions[J].Journal of Mathematical Research with Applications,2019,39(4):383-394.
Authors:Lizhen CHEN  Badawi Hamza Eibadawi IBRAHIM and Gang LI
Abstract:In this article, we consider the Bagley-Torvik type fractional differential equation $^{c}D^{\nu_1}l(t)-a^{c}D^{\nu_2}l(t)=g(t,l(t))$ and differential inclusion $^{c}D^{\nu_1}l(t)-a^{c}D^{\nu_2}l(t)\in G(t,l(t))$, $t\in (0,1)$ subjecting to $l(0)=l_0$, and $l(1)=\lambda''\int_0^{\omega}\frac{(\omega-s)^{\chi-1}l(s)}{\Gamma(\chi)}\d s$, where $1<\nu_1\leq 2$, $1\leq \nu_2<\nu_1$, $0<\omega\leq1$, $\chi=\nu_1-\nu_2>0$, $a$, $\lambda''$ are given constants. By using Leray-Schauder degree theory and fixed point theorems, we prove the existence of solutions. Our results extend the existence theorems for the classical Bagley-Torvik equation and some related models.
Keywords:fractional differential equations and inclusions  integral boundary conditions  Leray-Schauder theory
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