Abstract
In this paper, we study a system of Hadamard fractional multi-point boundary value problems. We first obtain triple positive solutions when the nonlinearities satisfy some bounded conditions. Next, we also obtain a nontrivial solution when the nonlinearities can be asymptotically linear growth. Furthermore, we provide two examples to illustrate our main results.
Highlights
We use some fixed point theorems to study the existence of solutions for the system of Hadamard fractional multi-point boundary value problems
In [11], Jiang et al adopted the fixed point index to study the existence of positive solutions for the system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions
(9) has at least one nontrivial solution
Summary
We use some fixed point theorems to study the existence of solutions for the system of Hadamard fractional multi-point boundary value problems. In [14], the authors studied the Riemann–Liouville fractional differential inclusion with Hadamard fractional integral boundary conditions. In [29], Zhang et al utilized the Guo–Krasnosel’skii fixed point theorem to obtain the multiple positive solutions for the Hadamard fractional integral boundary value problems. In [11], Jiang et al adopted the fixed point index to study the existence of positive solutions for the system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions.
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