Existence and uniqueness of solutions for a class of fractional nonlinear boundary value problems under mild assumptions

被引：5

作者：

Bachar, Imed ^{[1
]}

Maagli, Habib ^{[2
,3
]}

Eltayeb, Hassan ^{[1
]}

机构：

[1] King Saud Univ, Coll Sci, Math Dept, POB 2455, Riyadh 11451, Saudi Arabia

[2] King Abdulaziz Univ, Coll Sci & Arts, Dept Math, Rabigh Campus,POB 344, Rabigh 21911, Saudi Arabia

[3] Univ Tunis El Manar, Fac Sci Tunis, Modelisat Math Anal Harmon & Theorie Potentiel LR, Tunis 2092, Tunisia

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2021年 / 2021卷 / 01期

关键词：

Fractional differential equation; Green's function; Existence and uniqueness of solution; Banach's contraction principle;

D O I：

10.1186/s13662-020-03176-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We deal with the following Riemann-Liouville fractional nonlinear boundary value problem: integral D(alpha)v(x) + f (x, v(x)) = 0, 2 < alpha <= 3, x is an element of (0, 1), v(0) = v'(0) = v(1) = 0. Under mild assumptions, we prove the existence of a unique continuous solution v to this problem satisfying vertical bar v(x)vertical bar <= cx(alpha-1)(1 - x) for all x is an element of [0, 1] and some c > 0. Our results improve those obtained by Zou and He (Appl. Math. Lett. 74:68-73, 2017).

引用

页数：11

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