Positive solutions for singular higher-order semipositone fractional differential equations with conjugate type integral conditions

Abstract

In this article, height functions on different bounded sets of the nonlinear term and their integrations are considered to obtain the existence of positive solutions for a class of semipositone higher-order fractional differential equations with nonlocal conjugate type integral conditions. The singularities of the nonlinearity are related to both the time and the space variables.

Uniqueness of Successive Positive Solution for Nonlocal Singular Higher-Order Fractional Differential Equations Involving Arbitrary Derivatives

“…This article admits some new features. First, compared to [6][7][8][9][10][11][12][13][14][15][16] the problem considered in this paper performs more general form since another parameter is contained in boundary conditions. Second, the nonlinearity is not only singular on space variable but also relative with -order derivative of an unknown variable .…”