Existence of solutions for several higher-order Hadamard-type fractional differential equations with integral boundary conditions on infinite interval

Abstract

In this paper, we investigate the existence of solutions for several higher-order integral boundary value problems of Hadamard-type fractional differential equations on an infinite interval by using the monotone iterative technique and Mawhin's continuation theorem. The results enrich and extend some known conclusions of Hadamard-type fractional boundary value problems. Moreover, we give two concrete examples to illustrate the theoretical results.

Existence, uniqueness, and multiplicity results on positive solutions for a class of Hadamard‐type fractional boundary value problem on an infinite interval

“…In this article, we aim to obtain the existence, uniqueness, and multiplicity of positive solutions for BVP . To the authors' knowledge, while the Hadamard‐type fractional derivative is commonly considered for fractional BVPs, to date, few studies have considered BVPs of Hadamard‐type fractional differential equations on infinite intervals . Compared with existing papers, the new insights provided in this paper can be summarized as follows: First, we apply several different techniques to obtain our results including Schauder's fixed point theorem, Banach's contraction mapping principle, the monotone iterative method, and the Avery‐Peterson fixed point theorem.…”

“…Several research papers dealing with Hadamard-type fractional differential equations with various boundary conditions have been recently published. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] Refer to Ahmad et al 9 for a comprehensive monograph on Hadamard-type fractional differential equations, inclusions, and inequalities.…”

“…To the authors' knowledge, while the Hadamard-type fractional derivative is commonly considered for fractional BVPs, to date, few studies have considered BVPs of Hadamard-type fractional differential equations on infinite intervals. [22][23][24][25][26][27][28] Compared with existing papers, the new insights provided in this paper can be summarized as follows: First, we apply several different techniques to obtain our results including Schauder's fixed point theorem, Banach's contraction mapping principle, the monotone iterative method, and the Avery-Peterson fixed point theorem. Not only do we discuss the existence and uniqueness of positive solutions for BVP (1.1) but also the existence of two and three positive solutions for BVP (1.1).…”

Multiplicity of positive solutions for Hadamard fractional differential equations with p-Laplacian operator

“…The key of this definition involves a logarithmic function of arbitrary exponent. In the past decades, there were more studies on Hadamard fractional differential equations under different boundary conditions, see [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54].…”

“…where λ, a, b are three parameters, α, β ∈ (n -1, n] are two real numbers, and n ≥ 3, by applying Guo-Krasnoselskii's fixed point theorem. Zhang and Liu [47] investigated the existence of solutions for several higher order integral boundary value problems of Hadamardtype fractional differential equations on an infinite interval by using the monotone iterative technique and Mawhin's continuation theorem. In [48], Ahmad and Ntouyas discussed the following coupled Hadamard-type FDEs with Hadamard-type integral boundary conditions:…”