Existence of Positive Solutions for a Higher-Order Fractional Differential Equation with Multi-Term Lower-Order Derivatives

Weiwei Liu and Lishan Liu
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Weiwei Liu: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Lishan Liu: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Mathematics, 2021, vol. 9, issue 23, 1-23

Abstract: This paper deals with the study of the existence of positive solutions for a class of nonlinear higher-order fractional differential equations in which the nonlinear term contains multi-term lower-order derivatives. By reducing the order of the highest derivative, the higher-order fractional differential equation is transformed into a lower-order fractional differential equation. Then, combining with the properties of left-sided Riemann–Liouville integral operators, we obtain the existence of the positive solutions of fractional differential equations utilizing some weaker conditions. Furthermore, some examples are given to demonstrate the validity of our main results.

Keywords: fractional differential equation; boundary value problems; positive solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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