Multiple positive solutions to singular fractional differential equations with integral boundary conditions involving p−q $p-q$-order derivatives

Abstract

Abstract In this paper, we investigate the existence for a class of higher-order fractional differential equations with integral boundary value conditions involving p−q $p-q$-order derivatives. As an application of the height functions on some special bounded sets, we obtain the existence of two positive solutions by means of the Leray–Schauder nonlinear alternative and cone expansion and cone compression fixed point theory. The nonlinearity may take negative infinity, and there may appear a singular phenomenon on both time and space variables.

Keywords

• Nonlocal fractional differential equations
• Integral conditions
• Semipositone
• Singularity on space variable
• Positive solutions