| Nonlocal Integral Boundary Value Problem of Bagley-Torvik Type Fractional Differential Equations\\ and Inclusions |
| Received:June 02, 2018 Revised:April 11, 2019 |
| Key Words:
fractional differential equations and inclusions integral boundary conditions Leray-Schauder theory
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11571300; 11871064). |
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| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.04.006 |
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