Solvability for a system of Hadamard fractional multi-point boundary value problems

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.

Positive solutions for a Hadamard-type fractional p-Laplacian integral boundary value problem

“…In this section, we give the definition of the Hadamard-type fractional derivative; for more details, we refer the reader to [29][30][31][32].…”

Positive Solutions and Their Existence of a Nonlinear Hadamard Fractional-Order Differential Equation with a Singular Source Item Using Spectral Analysis

“…How to get the existence result of positive solution for the fractionalorder differential model as well as its related nonlinear dynamics becomes a hot research direction in the field of fractional-order differential models, and many meaningful results are achieved in recent years [12][13][14][15][16][17]. Xu et al [18] depicted the positive solutions of a kind of fractional-order differential models as follows H D α a + x(t) + h(t, x(t)) = 0, t ∈ (a, b), with the boundary value condition…”

“…a given function and ℓ(t, x, y) is continuous, and H D ♭ 1 + is the standard Hadamard derivative. Compared with [18,21], the present study contains the the derivative term in the nonlinear term of the equation and we will deal with this difficulty, moreover, and involved infinite points in the boundary conditions. Compared with [19], the nonlinear term is singular in this article, and the method we used is spectral analysis and infinite-points are contained in the boundary conditions.…”

Solvability for a Hadamard-type fractional integral boundary value problem

“…where ϑ ∈ (1,2]. In [24] the authors used the five functional fixed point theorems to study the multiplicity of positive solutions for the system of Hadamard fractional multipoint boundary value problems H D q 1 + u(t) + f 1 t, u(t), v(t) = 0, 1 < t < e, H D q 1 + v(t) + f 2 t, u(t), v(t) = 0, 1 < t < e,…”