Existence and multiplicity of positive solutions for a new class of singular higher-order fractional differential equations with Riemann–Stieltjes integral boundary value conditions

Abstract

Abstract In this work, the aim is to discuss a new class of singular nonlinear higher-order fractional boundary value problems involving multiple Riemann–Liouville fractional derivatives. The boundary conditions are constituted by Riemann–Stieltjes integral boundary conditions. The existence and multiplicity of positive solutions are derived via employing the Guo–Krasnosel’skii fixed point theorem. In addition, the main results are demonstrated by some examples to show their validity.

Keywords

• Fractional differential equations
• Riemann–Stieltjes integral boundary value problem
• Positive solutions
• Singular problem
• Fixed point theorem