Solvability of Sturm–Liouville boundary value problems for multiple order fractional differential equations

Abstract

In this paper, definitions of Lα1 function space, β-well function space and quasi-Carathéodory function are given, existence results for solutions of a class of Sturm–Liouville boundary value problems of fractional differential equations with multiple order derivatives D0+α[Φ(ρ(t)D0+βx(t))] are established. The analysis relies on a well known fixed point theorem. Some examples are given to illustrate the efficiency of main theorems.

Keywords

• Lα1 function space
• β-well function
• Multiple order fractional differential equation
• Sturm–Liouville boundary value problems
• Leray–Schauder Alternative principle