Positive Solutions of Eigenvalue Problems for a Class of Fractional Differential Equations with Derivatives

Abstract

By establishing a maximal principle and constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of a class of fractional differential equations is discussed. Some sufficient conditions for the existence of positive solutions are established.

Nonlocal fractional order differential equations with changing-sign singular perturbation

“…In recent years, fractional order differential equations arise in the modeling of many complex dynamic phenomena in viscoelasticity, rheology, fluid mechanics, electrical networks and chemical physics, and thus have attracted more and more attention in the scientific research communities [6][7]9,[11][12][13][14][15][16][17][18][19][20].…”

Positive solutions for eigenvalue problems of fractional differential equation with generalized p-Laplacian

“…To the best of our knowledge, some results were obtained dealing with the existence of positive solutions for the eigenvalue problem of fractional differential equations, see [15,23,30,31], but very little is known in the literature on the eigenvalue problems of fractional differential equation with generalized p-Laplacian operator. Its theories and applications seem to be just being initiated.…”

Positive Solutions of Fractional Differential Equation with -Laplacian Operator

“…Recently, fractional-order models have proved to be more accurate than integer-order models; that is, there are more degrees of freedom in the fractional-order models. So complicated dynamic phenomenon of fractional-order calculus system has received more and more attention; see [2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”