Abstract
This paper reports the investigation of eigenvalue problems for two classes of nonlinear fractional differential equations with generalized p-Laplacian operator involving both Riemann–Liouville fractional derivatives and Caputo fractional derivatives. By means of fixed point theorem on cones, some sufficient conditions are derived for the existence, multiplicity and nonexistence of positive solutions to the boundary value problems. Finally, an example is presented to further verify the correctness of the main theoretical results and illustrate the wide range of their potential applications.
Highlights
Eigenvalue problem is a class of homogeneous boundary value problems for differential equations with parameters
In the last few years, fractional differential equations have gained attentions due to their numerous applications in various aspects of science and technology. Eigenvalue problems and their applications are gradually beginning to be studied for fractional differential equations
In [8], Eloe et al used the theory of u0-positive operators to study boundary value problem for a class of linear fractional differential equations
Summary
Eigenvalue problem is a class of homogeneous boundary value problems for differential equations with parameters. In [8], Eloe et al used the theory of u0-positive operators to study boundary value problem for a class of linear fractional differential equations. In [12], eigenvalue comparison results of boundary value problems for linear fractional differential equations with the Caputo fractional derivative were obtained. In [11], Han et al investigated the existence of positive solutions to the following eigenvalue problem for nonlinear fractional differential equation with generalized p-Laplacian operator: D0β+ φ D0α+ u(t) = λf u(t) , 0 < t < 1, u(0) = u (0) = u (1) = 0, φ D0α+ u(0) = φ D0α+ u(1) = 0, Nonlinear Anal.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
