The Nehari manifold for a boundary value problem involving Riemann-Liouville fractional derivative

被引：38

作者：

Saoudi, Kamel ^{[1
]}

Agarwal, Praveen ^{[2
,3
]}

Kumam, Poom ^{[4
,5
]}

Ghanmi, Abdeljabbar ^{[6
]}

Thounthong, Phatiphat ^{[7
,8
]}

机构：

[1] Univ Dammam, Coll Sci Dammam, Dammam, Saudi Arabia

[2] Int Ctr Basic & Appl Sci, Jaipur, Rajasthan, India

[3] Anand Int Coll Engn, Dept Math, Jaipur, Rajasthan, India

[4] KMUTT, Fac Sci, Dept Math, KMUTTFixed Point Res Lab, Room SCL 802, Bangkok, Thailand

[5] KMUTT, Fac Sci, Theoret & Computat Sci Ctr TaCS, Fixed Point Theory & Applicat Res Grp, Sci Lab Bldg, Bangkok, Thailand

[6] Univ Jeddah, Fac Sci & Arts, Math Dept, Jeddah, Saudi Arabia

[7] KMUTNB, Fac Tech Educ, Renewable Energy Res Ctr, Bangkok, Thailand

[8] KMUTNB, Fac Tech Educ, Dept Teacher Training Elect Engn, Bangkok, Thailand

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2018年

关键词：

Nonlinear fractional differential equations; Riemann-Liouville and Caputo fractional derivative; Critical point theory; Existence of solutions; Method of Nehari manifold; EXISTENCE; CALCULUS;

D O I：

10.1186/s13662-018-1722-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We aim to investigate the following nonlinear boundary value problems of fractional differential equations: (P lambda){-D-t(1)alpha (vertical bar D-0(t)alpha(u(t))vertical bar(p-2)(0)D(t)(alpha)u(t)) = f (t,u(t)) +lambda g(t)vertical bar u(t)vertical bar(q-2)u(t) (t is an element of(0, 1)), u(0) = u(1) = 0, where. is a positive parameter, 2 < r < p < q, 1/2 < alpha < 1, g is an element of C([0, 1]), and f is an element of C([0, 1] xR, R). Under appropriate assumptions on the function f, we employ the method of Nehari manifold combined with the fibering maps in order to show the existence of solutions to the boundary value problem for the nonlinear fractional differential equations with Riemann- Liouville fractional derivative. We also present an example as an application.

引用

页数：18

共 33 条

[21]

Khan R. A., 2011, FRACTIONAL DIFFERENT, V1, P29, DOI DOI 10.7153/FDC-01-02

[22] Existence - uniqueness result for a certain equation of motion in fractional mechanics [J].